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Intro to GMAT Word Problems, Part 2: Assigning Variables [#permalink]

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New post 05 May 2016, 16:01
FROM Magoosh Blog: Intro to GMAT Word Problems, Part 2: Assigning Variables
This article is continued from the first, on “Translating from Words to Math.”  First of all, here are four word problems that present issues with assigning variables.

1) Each month, after Jill pays for rent, utilities, food, and other necessary expenses, she has one fifth of her net monthly salary left as discretionary income.  Of this discretionary income, she puts 30% into a vacation fund, 20% into savings, and spends 35% on eating out and socializing.  This leaves her with $96 dollar, which she typically uses for gifts and charitable causes.  What is Jill’s net monthly salary?

(A) $2400

(B) $3200

(C) $6000

(D) $6400

(E) $9600

 

2) Right now, Al and Eliot have bank accounts, and Al has more money than Eliot.  The difference between their two accounts is 1/12 of the sum of their two accounts.  If Al’s account were to increase by 10% and Eliot’s account were to increase by 20%, then Al would have exactly $22 more than Eliot in his account.  How much money does Eliot have in his account right now?

(A) $110

(B) $120

(C) $180

(D) $220

(E) $260

Image

3) A pool, built with one edge flush against a building, has a length that is 5 meters longer than its width.  The short width is against the building.  A 4 meter wide path is built on three side around the pool, as shown in the diagram (the path is yellow).  If the area of the path is 216 sq m, what is the width of the pool in meters?

(A) 12

(B) 14

(C) 16

(D) 18

(E) 20

 

4) Four friends, Saul, Peter, Quirinal, and Roderick, are pooling their money to buy a $1000 item.  Peter has twice as much money as Saul.  Quirinal has $60 more than Peter.  Roderick has 20% more than Quirinal.  If they put all their money together and spend the $1000, they will have $20 left.  How much money does Peter have?

(A) $120

(B) $160

(C) $180

(D) $200

(E) $240

Full solutions will appear at the end of this article.

 

Assigning Variables
Most GMAT word problem concern real world quantities and are stated in real world terms, and we need to assign algebraic variables to these real world quantities.

Sometimes, one quantity is directly related to every other quantity in the problem.  For example:

“Sarah spends 2/5 of her monthly salary on rent, 1/12 of her monthly salary on auto costs including gas and insurance, and 1/10 of her monthly salary automatically goes into saving each month.  With what she has left each month, she spend she spends $800 on groceries and …”

In that problem, everything is related to “monthly salary,” so it would make a lot of sense to introduce just one variable for that, and express everything else in terms of that variable.  Also, please don’t always use the boring choice of x for a variable!  If we want a variable for salary, you might use the letter S, which will help you remember what the variable means!  If we are given multiple variables that are all related to each other, it’s often helpful to assign a letter to the variable with the lowest value, and then express everything else in terms of this letter.

If there are two or more quantities that don’t depend directly on each other, then you may well have to introduce a different variable for each.  Just remember that it’s mathematically problematic to litter a problem with a whole slew of different variables.  You see, for each variable, you need an equation to solve it.  If we want to solve for two different variables, we need two different equations (this is a common Word Problem scenario).  If we want to solve for three different variables, we need three different equations (considerably less common).  While the mathematical pattern continues to extend upward from there, more than three completely separate variables is almost unheard of on GMAT math.

When you assign variables, always be hyper-vigilant and over-the-top explicit about exactly what each variable means.  Write a quick note to yourself on the scratch paper: T = the price of one box of tissue, or whatever the problem wants.  What you want to avoid is the undesirable situation of solving for a number and not knowing what that number means in the problem!

Here’s an easier-than-the-GMAT word problem as an example:

“Andrew and Beatrice each have their own savings account.  Beatrice’s account has $600 less than three times what Andrew’s account has.  If Andrew had $300 more dollars, then he would have exactly half what is currently in Beatrice’s account.  How much does Beatrice have?”

The obvious choices for variables are A = the amount in Andrew’s account and B = the amount in Beatrice’s account.  The GMAT will be good about giving you word problems involving people whose names start with different letter, so that it’s easier to assign variables.  We can turn the second & third sentences into equations.

second sentence: B = 3A – 600

Image

Both equations are solved for B, so simply set them equal.

3A – 600 = 2(A + 300)

3A – 600 = 2A + 600

A – 600 = 600

A = 1200

We can plug this into either equation to find B.  (BTW, if you have time, an excellent check is to plug it into both equations, and make sure the value of B you get is the same!)

B = 3000

Thus, Andrew has $1200 in his account, and Beatrice, $3000 in hers.

 

Summary
If the foregoing discussion gave you any insights into assigning variables, it may well be worthwhile to look at those four practice problems again before preceding to the explanations below.   If you join Magoosh, you can watch our 20+ video lessons on Word Problems.

Image

 

Explanations to Practice Problems
1) Everything is in terms of Jill’s discretionary income, which is one-fifth of the net monthly rent.  It makes sense to assign a variable to the former, solve for it, and then compute the latter.  I will assign the letter D, to remind us that this represents the monthly discretionary income, not the answer to the question.  We will not yet have the answer when we find the value of D.

vacation = 30% of D

savings = 20% of D

eating out & socializing = 35% of D

Together, those account for 85% of her monthly discretionary income.  That leaves 15%.  This 15% equals $96.

15% of D = $96

Divide by sides by 3.

5% of D = $32

Double.

10% of D = $64

Now, multiply by 10.

100% of D = D = $640

Remember, this is the value of D, the monthly discretionary income, not what the question asked.  The question wanted monthly salary, which is five times this.  Well, ten times D is $6400, so five times D would be half of that, $3200.

Answer = (B)

 

2) Names in this problem from a famous Al and a famous Eliot.  Let’s start with two variables, A and E.  The difference (A – E) is 1/12 the sum (A + B).

12(A – E) = A + E

12A – 12E = A + E

11A = 13E

Now, since we have related these variables, it doesn’t make sense to move through the rest of problem with two different variables.  We could express E = (11/13)*A, and express everything in terms of A, but 11/13 is an especially ugly fraction.  Here’s an alternative, using a little number sense.   Clearly A equals 13 parts of something, and E equals 11 parts of something.  Let’s say that P = the “part” in this ratio; then A = 13P and E = 11P.  We can express everything in terms of P.

Al’s account increases by 10%:

New Al = 1.10*(13*P) = 14.3*P

Eliot’s account increases by 20%:

New Eliot = 1.20*(11*P) = 13.2*P

Difference = 14.3*P – 13.2*P = 1.1*P = $22

Multiply both sides by 10 to clear the decimal.

11*P = $220

We could solve for P at this point, but notice that what we want, Eliot’s amount, is already equal to 11*P.  This is the answer!  Eliot has $220 in his account.

Answer = (D)

3) Call the width W.  Then the length is L = W + 5.  The section of path to the left of the pool in the diagram is a rectangle L tall and 4 wide, so it’s area is

A1 = 4L = 4(W + 5)

In the upper-left hand corner of the path, there’s a 4 x 4 square, with area:

A2 = 16

Above the pool is a rectangle with a height of 4 and width of W, with an area:

A3 = 4W

Another 4 x 4 square in the upper right-hand corner:

A4 = 16

And finally, another rectangle on the right, equal to the one on the left

A5 = A1 = 4(W + 5)

All these pieces add up to 216.

Total = A1 + A2 + A3 + A4 + A5

Total = (4W + 20) + 16 + 4W + 16 + (4W + 20)

Total = 12W + 72 = 216

12W = 216 – 72 = 144

W = 12

The pool has a width of 12 m and a length of 17 m.

Answer = (A)

4) Saul appears to have the least money, so we will put everything in terms of his amount.

P = 2*S

Q = P + 60 = 2*S + 60

R = 1.2*Q = 1.2*(2*S + 60) = 2.4*S + 72

Total = S + P + Q + R

Total = S + 2*S + 2*S + 60 + 2.4*S + 72

Total = 7.4*S + 132 = 1020

7.4*S = 888

74*S = 8880

37*S = 4440

At this point, it’s very helpful to know that 3*37 = 111.  This means that 12*37 = 444, and 120*37 = 4440.  Thus, S = 120.  Saul has $120.  Notice, though, the question is not asking for what Saul has: it is asking for what Peter has.  Peter has twice Saul’s amount, so Peter has $240.

Answer = (E)

This is beyond what you need to know for the test, but in this problem there’s a pattern encrypted in the names.  The abbreviation of the four names spells out SPQR, which was the abbreviation in Latin for the name of the Roman Empire (Senatvs Popvlvsqve Romanvs = “The Senate and the People of Rome”).  The four names are folks associated with the city of Rome in one way or another.  In the Christian tradition, Saul (who became St. Paul) and St. Peter are believed to have lived and died in Rome.  The somewhat obscure male name Quirinal was the name of a son of the god Mars, and it is also the name of the one of the seven hills of Rome.  The name Roderick is an inside-joke from a Monty Python film set during Roman times.

 

The post Intro to GMAT Word Problems, Part 2: Assigning Variables appeared first on Magoosh GMAT Blog.
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

_________________

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Magoosh Test Prep

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Intro to GMAT Word Problems, Part 2: Assigning Variables [#permalink]

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New post 05 May 2016, 17:01
FROM Magoosh Blog: Intro to GMAT Word Problems, Part 2: Assigning Variables
This article is continued from the first, on “Translating from Words to Math.”  First of all, here are four word problems that present issues with assigning variables.

1) Each month, after Jill pays for rent, utilities, food, and other necessary expenses, she has one fifth of her net monthly salary left as discretionary income.  Of this discretionary income, she puts 30% into a vacation fund, 20% into savings, and spends 35% on eating out and socializing.  This leaves her with $96 dollar, which she typically uses for gifts and charitable causes.  What is Jill’s net monthly salary?

(A) $2400

(B) $3200

(C) $6000

(D) $6400

(E) $9600

 

2) Right now, Al and Eliot have bank accounts, and Al has more money than Eliot.  The difference between their two accounts is 1/12 of the sum of their two accounts.  If Al’s account were to increase by 10% and Eliot’s account were to increase by 20%, then Al would have exactly $22 more than Eliot in his account.  How much money does Eliot have in his account right now?

(A) $110

(B) $120

(C) $180

(D) $220

(E) $260

Image

3) A pool, built with one edge flush against a building, has a length that is 5 meters longer than its width.  The short width is against the building.  A 4 meter wide path is built on three side around the pool, as shown in the diagram (the path is yellow).  If the area of the path is 216 sq m, what is the width of the pool in meters?

(A) 12

(B) 14

(C) 16

(D) 18

(E) 20

 

4) Four friends, Saul, Peter, Quirinal, and Roderick, are pooling their money to buy a $1000 item.  Peter has twice as much money as Saul.  Quirinal has $60 more than Peter.  Roderick has 20% more than Quirinal.  If they put all their money together and spend the $1000, they will have $20 left.  How much money does Peter have?

(A) $120

(B) $160

(C) $180

(D) $200

(E) $240

Full solutions will appear at the end of this article.

 

Assigning Variables
Most GMAT word problem concern real world quantities and are stated in real world terms, and we need to assign algebraic variables to these real world quantities.

Sometimes, one quantity is directly related to every other quantity in the problem.  For example:

“Sarah spends 2/5 of her monthly salary on rent, 1/12 of her monthly salary on auto costs including gas and insurance, and 1/10 of her monthly salary automatically goes into saving each month.  With what she has left each month, she spend she spends $800 on groceries and …”

In that problem, everything is related to “monthly salary,” so it would make a lot of sense to introduce just one variable for that, and express everything else in terms of that variable.  Also, please don’t always use the boring choice of x for a variable!  If we want a variable for salary, you might use the letter S, which will help you remember what the variable means!  If we are given multiple variables that are all related to each other, it’s often helpful to assign a letter to the variable with the lowest value, and then express everything else in terms of this letter.

If there are two or more quantities that don’t depend directly on each other, then you may well have to introduce a different variable for each.  Just remember that it’s mathematically problematic to litter a problem with a whole slew of different variables.  You see, for each variable, you need an equation to solve it.  If we want to solve for two different variables, we need two different equations (this is a common Word Problem scenario).  If we want to solve for three different variables, we need three different equations (considerably less common).  While the mathematical pattern continues to extend upward from there, more than three completely separate variables is almost unheard of on GMAT math.

When you assign variables, always be hyper-vigilant and over-the-top explicit about exactly what each variable means.  Write a quick note to yourself on the scratch paper: T = the price of one box of tissue, or whatever the problem wants.  What you want to avoid is the undesirable situation of solving for a number and not knowing what that number means in the problem!

Here’s an easier-than-the-GMAT word problem as an example:

“Andrew and Beatrice each have their own savings account.  Beatrice’s account has $600 less than three times what Andrew’s account has.  If Andrew had $300 more dollars, then he would have exactly half what is currently in Beatrice’s account.  How much does Beatrice have?”

The obvious choices for variables are A = the amount in Andrew’s account and B = the amount in Beatrice’s account.  The GMAT will be good about giving you word problems involving people whose names start with different letter, so that it’s easier to assign variables.  We can turn the second & third sentences into equations.

second sentence: B = 3A – 600

Image

Both equations are solved for B, so simply set them equal.

3A – 600 = 2(A + 300)

3A – 600 = 2A + 600

A – 600 = 600

A = 1200

We can plug this into either equation to find B.  (BTW, if you have time, an excellent check is to plug it into both equations, and make sure the value of B you get is the same!)

B = 3000

Thus, Andrew has $1200 in his account, and Beatrice, $3000 in hers.

 

Summary
If the foregoing discussion gave you any insights into assigning variables, it may well be worthwhile to look at those four practice problems again before preceding to the explanations below.   If you join Magoosh, you can watch our 20+ video lessons on Word Problems.

Image

 

Explanations to Practice Problems
1) Everything is in terms of Jill’s discretionary income, which is one-fifth of the net monthly rent.  It makes sense to assign a variable to the former, solve for it, and then compute the latter.  I will assign the letter D, to remind us that this represents the monthly discretionary income, not the answer to the question.  We will not yet have the answer when we find the value of D.

vacation = 30% of D

savings = 20% of D

eating out & socializing = 35% of D

Together, those account for 85% of her monthly discretionary income.  That leaves 15%.  This 15% equals $96.

15% of D = $96

Divide by sides by 3.

5% of D = $32

Double.

10% of D = $64

Now, multiply by 10.

100% of D = D = $640

Remember, this is the value of D, the monthly discretionary income, not what the question asked.  The question wanted monthly salary, which is five times this.  Well, ten times D is $6400, so five times D would be half of that, $3200.

Answer = (B)

 

2) Names in this problem from a famous Al and a famous Eliot.  Let’s start with two variables, A and E.  The difference (A – E) is 1/12 the sum (A + B).

12(A – E) = A + E

12A – 12E = A + E

11A = 13E

Now, since we have related these variables, it doesn’t make sense to move through the rest of problem with two different variables.  We could express E = (11/13)*A, and express everything in terms of A, but 11/13 is an especially ugly fraction.  Here’s an alternative, using a little number sense.   Clearly A equals 13 parts of something, and E equals 11 parts of something.  Let’s say that P = the “part” in this ratio; then A = 13P and E = 11P.  We can express everything in terms of P.

Al’s account increases by 10%:

New Al = 1.10*(13*P) = 14.3*P

Eliot’s account increases by 20%:

New Eliot = 1.20*(11*P) = 13.2*P

Difference = 14.3*P – 13.2*P = 1.1*P = $22

Multiply both sides by 10 to clear the decimal.

11*P = $220

We could solve for P at this point, but notice that what we want, Eliot’s amount, is already equal to 11*P.  This is the answer!  Eliot has $220 in his account.

Answer = (D)

3) Call the width W.  Then the length is L = W + 5.  The section of path to the left of the pool in the diagram is a rectangle L tall and 4 wide, so it’s area is

A1 = 4L = 4(W + 5)

In the upper-left hand corner of the path, there’s a 4 x 4 square, with area:

A2 = 16

Above the pool is a rectangle with a height of 4 and width of W, with an area:

A3 = 4W

Another 4 x 4 square in the upper right-hand corner:

A4 = 16

And finally, another rectangle on the right, equal to the one on the left

A5 = A1 = 4(W + 5)

All these pieces add up to 216.

Total = A1 + A2 + A3 + A4 + A5

Total = (4W + 20) + 16 + 4W + 16 + (4W + 20)

Total = 12W + 72 = 216

12W = 216 – 72 = 144

W = 12

The pool has a width of 12 m and a length of 17 m.

Answer = (A)

4) Saul appears to have the least money, so we will put everything in terms of his amount.

P = 2*S

Q = P + 60 = 2*S + 60

R = 1.2*Q = 1.2*(2*S + 60) = 2.4*S + 72

Total = S + P + Q + R

Total = S + 2*S + 2*S + 60 + 2.4*S + 72

Total = 7.4*S + 132 = 1020

7.4*S = 888

74*S = 8880

37*S = 4440

At this point, it’s very helpful to know that 3*37 = 111.  This means that 12*37 = 444, and 120*37 = 4440.  Thus, S = 120.  Saul has $120.  Notice, though, the question is not asking for what Saul has: it is asking for what Peter has.  Peter has twice Saul’s amount, so Peter has $240.

Answer = (E)

This is beyond what you need to know for the test, but in this problem there’s a pattern encrypted in the names.  The abbreviation of the four names spells out SPQR, which was the abbreviation in Latin for the name of the Roman Empire (Senatvs Popvlvsqve Romanvs = “The Senate and the People of Rome”).  The four names are folks associated with the city of Rome in one way or another.  In the Christian tradition, Saul (who became St. Paul) and St. Peter are believed to have lived and died in Rome.  The somewhat obscure male name Quirinal was the name of a son of the god Mars, and it is also the name of the one of the seven hills of Rome.  The name Roderick is an inside-joke from a Monty Python film set during Roman times.

 

The post Intro to GMAT Word Problems, Part 2: Assigning Variables appeared first on Magoosh GMAT Blog.
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

_________________

Mike McGarry
Magoosh Test Prep

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Kudos [?]: 8152 [0], given: 100

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GMAT Tuesday: Official Guide Reading Comprehension #102 [#permalink]

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New post 10 May 2016, 12:02
FROM Magoosh Blog: GMAT Tuesday: Official Guide Reading Comprehension #102
Come learn how to tackle this special type of inference question—author’s purpose.



If you’d like to see how we evaluated the passage, head over to our first Reading Comprehension video in this series.

The post GMAT Tuesday: Official Guide Reading Comprehension #102 appeared first on Magoosh GMAT Blog.
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Kudos [?]: 8152 [0], given: 100

Expert Post
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4367

Kudos [?]: 8152 [0], given: 100

Logical Splits on GMAT Sentence Correction [#permalink]

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New post 17 May 2016, 17:02
FROM Magoosh Blog: Logical Splits on GMAT Sentence Correction
First, here are 8 GMAT Sentence Correction problems, each involving some kind of logical issue.

 

1) Napoleon entered Russia in June, 1812, with an army half a million strong, but leaving in December, 1812, with just less than 30,000 troops.

(A) leaving in December, 1812, with just less

(B) just left in December, 1812, with fewer

(C) left in December, 1812, with just less

(D) left just in December, 1812, with less

(E) left in December, 1812, with just fewer

 

2) In the early 1800s, seven planets were known, but perturbations in the orbit of Uranus, the seventh planet, suggesting the existence of a hypothetically eighth planet.

(A) suggesting the existence of a hypothetically

(B) suggesting the existence of a hypothetical

(C) to suggest the existence of a hypothetical

(D) suggested the existence of a hypothetical

(E) suggested the existence of a hypothetically

 

 

3) Potassium, whose outer electron is easily lost, is a highly reactive metal.

(A) Potassium, whose outer electron is easily lost, is a highly reactive metal

(B) Potassium is a highly reactive metal, it has an outer electron that is easily lost

(C) A highly reactive metal, potassium, with an outer electron that is easily lost

(D) The outer election of potassium, a highly reactive metal, is easily lost.

(E) A highly reactive metal that easily loses its outer electron is named “potassium.”

 

 

4) Although Bryant was better at gaining the support of rural voters than was McKinley, people who believed a silver-based economy would bring prosperity, McKinley won the 1896 election on a strong industry-based vote.

(A) Bryant was better at gaining the support of rural voters than was McKinley

(B) Bryant was better gaining the support of rural voters than McKinley

(C) Bryant was better than McKinley at gaining the support of rural voters

(D) compared to McKinley, Bryant had gained the support of rural voters more effectively

(E) unlike McKinley, Bryant was better at gaining the support of rural voters

 

 

5) Since the discovery of the Tufted Badger and other species in the ecosystems outside Vancouver, the number of riparian mammals in the Pacific Northwest has increased considerably.

(A) Since the discovery of the Tufted Badger and other species in the ecosystems outside Vancouver, the number of riparian mammals

(B) Since the Tufted Badger and other species in the ecosystems outside Vancouver have been discovered, the number of riparian mammals

(C) Because the Tufted Badger and other species in the ecosystems outside Vancouver have been discovered, the total riparian mammal number

(D) With the discovery of the Tufted Badger and other species in the ecosystems outside Vancouver, the number of known riparian mammals

(E) With the discovery of the Tufted Badger, as well as other species, in the ecosystems outside Vancouver, the number of riparian mammals

 

 

6) Developing East Asian information technology sectors, especially the ones in Vietnam, have been found by a consulting firm to be potential consumers for Cystar’s Hyperfast Server systems.

(A) Developing East Asian information technology sectors, especially the ones in Vietnam, have been found by a consulting firm to be potential consumers to Cystar’s Hyperfast Server systems

(B) According to a consulting firm, developing East Asian information technology sectors, particularly Vietnam, would be potential consumers for Cystar’s Hyperfast Server systems

(C) The potential consumers of Cystar’s Hyperfast Server systems are, according to a consulting firm, are the developing East Asian information technology sectors, particularly those in Vietnam.

(D) Cystar’s Hyperfast Server systems has potential customers in the the developing East Asian information technology sectors, particularly those in Vietnam according to a consulting firm

(E) A consulting firm has found that developing East Asian information technology sectors, particularly in Vietnam, would be potential consumers of Cystar’s Hyperfast Server systems

 

 

7) In the recent incidents of gang violence, it is the fact that innocent people were injured that has especially troubled the city leaders.

(A) In the recent incidents of gang violence, it is the fact that innocent people were injured that has especially troubled the city leaders

(B) The city leaders were especially troubled by the innocent people who were injured in the recent incidents of gang violence

(C) The innocent people, injured in the recent incidents of gang violence, especially troubled the city leaders

(D) In the recent incidents of gang violence, it is a fact that innocent people were injured and that the city leaders were especially troubled

(E) In the recent incidents of gang violence, innocent people were in fact injured, and this has especially troubled the city leaders

 

8) The Treaty of Utrecht, a series of documents signed in 1713, brought a peace that put an end to the plan of Louis XIV of France to upset the balance of power in Europe by gaining significant influence over the Spanish Empire.

(A) The Treaty of Utrecht, a series of documents signed in 1713, brought a peace that put an end to the plan of Louis XIV of France to upset the balance of power in Europe by gaining significant influence over the Spanish Empire

(B) The Treaty of Utrecht, a series of documents signed in 1713, bringing peace by putting an end to the plan of Louis XIV of France, who wanted to upset the balance of power in Europe when he gained significant influence in the Spanish Empire

(C) A series of documents signed in 1713, known as the Treaty of Utrecht, restored peace to Europe by putting an end to the plan of Louis XIV of France, who, in gaining significant influence over the Spanish Empire, wanted to upset the balance of power in Europe

(D) The balance of power in Europe was threatened when Louis XIV of France tried to gain significant influence in the Spanish Empire; therefore the Treaty of Utrecht, a series of documents signed in 1713, restored the peace by ending this plan

(E) Louis XIV of France planned to upset the balance of power in Europe by gaining significant influence with the Spanish Empire, but in 1713, a series of documents known as the Treaty of Utrecht was signed, and this put a peaceful end to the plan

 

Explanations for these questions will come at the end of this article.

 

Logic on the GMAT Sentence Correction
Some students naïvely believe that the GMAT Sentence Correction tests only grammar, and these students believe that by mastering grammar, they can master the SC questions.  This view is mistaken.  In fact, grammar, logic, and rhetoric all play a role.  Here are a few previous blogs that address logical issues on the GMAT Sentence Correction.

a) Logical Predication on the GMAT Sentence Correction

b) GMAT Sentence Correction: Indefinite Pronouns and Logic

c) Logical Splits in GMAT Sentence Correction

It’s very important that the precise logical meaning of the sentence reflect what the sentence is trying to say.  Many times in colloquial English, people say something that conveys meaning informally even though, rigorously, it is not logical.  Many of the logic mistakes on the GMAT reflect this: we can tell what the sentence means, despite what it is saying.  For the GMAT, a good sentence is one in which grammar and logic and rhetoric are all working together to convey a single meaning.

Since many GMAT takers overemphasize grammar and neglect logic, at least one or two answer choices on many SC questions are 100% grammatically correct but logically flawed.  Some of the answer choices above follow this pattern.  Once again, mastery of GMAT Sentence Correction requires understanding how grammar, logic, and rhetoric all work together and support each other.

 

Summary
If anything said here, or anything in those linked blogs, gave you any insights, then you may want to look over some of the questions again before studying the explanations below.   Think about logic in the writing you observe.  Advertisements are wonderful places to see blatant logical errors. Also, observe how high-quality, sophisticated writers use logical precision to make their points.

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Practice Problem Explanations
1) Split #1: countable vs. uncountable.  Troops are countable, so we need to use “fewer,” not “less.”  We can eliminate (A), (C), and (D) on the basis of this error.

Split #2: One of the more subtle logical splits on GMAT Sentence Correction involves the placement of adverb modifiers.  In this sentence, where should the “just” fall?  What do we want to denote as significantly limited?  Choice (B) has “just left,” as if we expected Napoleon to do something else, something more complicated or exalted, than the act of leaving; that interpretation is not the meaning, because the sentence is not contrasting the intensity of that action with any other.

By contrast, “just fewer than 30,000” retains the meaning of the prompt and emphasizes the shocking reduction in Napoleon’s army, which is the point of the sentence.

The best answer is (E).

 

2) A question about the events that led to the discovery of Neptune in 1846.

Split #1: the famous missing-verb mistake.  In the overall organization of the sentence, we have a first independent clause, “seven planets were known,” then the conjunction “but,” which signals another independent clause coming.  For this second independent clause, we get a noun for the subject, “perturbations in the orbit of Uranus,” and we need a full bonafide verb.  Choices (A) & (B) give us a participle, and choice (C) gives us an infinitive, but these won’t do.  We need the full verb “suggested,” which appears in (D) & (E).  We can eliminate (A) & (B) & (C).

Split #2: One kind of logic split involves the choice between an adjective and its corresponding adverb.  Here, we have to choose between “hypothetical” and “hypothetically.”

As an adjective, it would have to modify the noun.  If we say “a hypothetical eighth planet,” then we are saying that we don’t know whether the planet exists, but if it did exist after the first seven, of course it would be the eighth.

As an adverb, it would have to modify the adjective.  If we say “a hypothetically eighth planet,” then we are saying that we are not sure where the planet would fall in the numbering system: it could be the eighth or could be some other number; in this phrasing, it sounds as if the numbering is in doubt, but not the existence of the planet itself.

What was actually in doubt at that moment in history was the planet itself.  Of course, if it came after the first seven planets, it would be the eighth: that much was not in doubt.  The existence of the planet was in doubt.  The adjective “hypothetical” reflects this meaning.  We can reject the choices with “hypothetically,” choices (A) and (E).

The only possible answer is (D).

 

3) A question about potassium, the 19th element on the Periodic Table.  The five answers are all different, so we must treat each separately.

(A) Use of the possessive “whose” is perfectly fine either for a person or for an inanimate object.  This option is grammatically and logically correct.  This is a promising choice.

(B) This option is a run-on sentence with a comma splice.   This is incorrect.

(C) This option commits the famous missing-verb mistake.  We get a main subject, “a highly reactive metal,” and this subject never gets a full verb.  This is incorrect.

(D) This is grammatically correct but awkward.  It makes the electron, rather than potassium the element, the focus of the sentence, which casts the entire sentence into the passive.  This is far from ideal.

(E) This choice is logically incorrect.  It implies that any “highly reactive metal that easily loses its outer electron” would be called potassium, as if potassium were the name of a category of metals with similar properties, rather than a single metal.  While you don’t need to understand chemistry (see below), you do need to keep the meaning consistent with the prompt.  The prompt identifies potassium as a single metal, so we have to stick with that interpretation.

Choice (D) is a questionable answer, so (A) is by far the best answer here.

 

BTW, this is more than you need to know for the GMAT, but if you are interested in the chemistry, then on the Periodic Table of the Elements, all the IA elements below hydrogen are highly reactive metals that easily lose an outer electron.  These include lithium, sodium, potassium, rubidium, and caesium (a radioactive liquid that explodes on contact with air or water!)  Potassium is the name of one metal in this category, not the name of the category.  Sometimes the category is known as the Alkali Metals or the IA Elements.

 

4) A question about William Jennings Bryan and President William McKinley.

Split #1: the underlined section is followed by the appositive phrase “people who believed a silver-based economy would bring prosperity.”  These people are the rural voters, so this modifier must touch “rural voters.”  Where this modifier touches McKinley, it is a misplaced modifier, illogically equating this person to “people.”  Choices (A) & (B) make this mistake.

Let’s look at the three remaining choices.

(C) This is grammatically and logically sound.  This is a promising choice.

(D) This is an unidiomatic and awkward comparison, “compared to A, B is more X.”  While technically correct, we can reject this because there are more elegant possibilities.

(E) This is an illogical comparison.  We could say, “Unlike B, A is good at X,” which tells us that there is no question of degree: A is good at X, and B is not.  Alternative, we could say ” A is better at X than is B,” which tells us that it’s a question of degree: both are good, but A is better.   Choice (E) mixes elements of either comparison to create a logically ambiguous comparison: we get that Bryan is better, but was McKinley not good at all or simply not as good as Bryan??  Choice (E) is illogical and wrong.

The best answer is choice (C).

 

5) This question contains a very subtle logical split.  Let’s think about this.  In this natural ecosystem outside of Vancouver, there are some number of riparian mammals living out in Nature, just doing what they are doing.  Whether they live or die, thrive or fail, depends on a host of natural factors but most certainly does not depend on what the scientists know or don’t know.  Thus, when scientific researchers make a new discovery, the actual number of mammals out in the world does not change—all that changes is our knowledge!  It is the height of our arrogance as a species to think that some change in our knowledge actually changes anything in the natural world around us!   The number of riparian mammals doesn’t change: all that changes is the number of known riparian mammals. In other words, mammals that were there all along have crossed in our human scientific categories from unknown to known.  The only choice that reflect his perspective is (D), the OA.

 

6) One of the logic splits in this problem concerns the way Vietnam is mentioned.  The problem discusses “East Asian information technology sectors” and wants to cite the specific example of the information technology sectors in Vietnam.  Notice how this appears in the five choices.

(A) Here, “the ones in Vietnam” is a little informal but logically and grammatically correct.   The overall passive structure of this choice makes it weak and mealy mouthed.  It is technically correct but undesirable.  We hope there is something better so that we don’t have to settle for this.

(B) The phrase “particularly Vietnam” is an illogical comparison: it makes Vietnam the country sound like nothing more than an information technology sectors.  Choice (B) is illogical and incorrect.

(C) In this choice, the mention of Vietnam is fine, but the entire choice changes the meaning.  The prompt suggested that the “developing East Asian information technology sectors” are one possibility for customers, but it doesn’t exclude the possibility that other potential customers are elsewhere in the world.  The phasing in (C) makes the possibility exclusive, suggesting that these East Asian possibilities are the only possibilities for new customers.   That’s an unwarranted change in meaning, so (C) is incorrect.

(D) This choice changes the meaning in a different way.  The mention of Vietnam is logically correct, but the placement of “according to a consulting firm” makes it sound as if only the Vietnam case were the substance of the consulting firm’s recommendation, rather than the entire East Asian theater.  In other words, the exact information provided by the consulting firm is different in this choice.  This is also a change in meaning, so (D) is also incorrect.

(E) This choice is entirely correct, both logically and grammatically. It is direct, crisp, and clear, a powerful rhetorical statement.  Notice that the mention of Vietnam elegantly uses a parallel structure that omits common words.   This is a masterpiece of concision and clarity.  This choice is much better than (A).  Choice (E) is the best answer.

 

7) Split #1: One logical split in this problem concerns what actually troubled the city leaders?  The innocent people themselves did not trouble the city leaders.  The fact that innocent people were injured is what troubled the city leaders.  Although both grammatically correct, choices (B) & (C) make the mistake of implying that the innocent people themselves were troubling: this is illogical, and these two choices are incorrect.

Split #2: pronoun problem.  The pronoun “this” in choice (E) is problematic.  Everything up to the second comma is fine, but then the pronoun “this” refers to the action of the previous clauses.  Pronouns must have nouns as their antecedents: pronouns can’t refer to the action of a verb.   This is an invalid use of pronouns, and choice (E) is incorrect.

Split #3: logical cohesion.  Entirely grammatically correct, choice (D) presents the two facts side-by-side, (1) innocent people were injured, and (2) city leaders are troubled.  The relationship between these two facts is not made clear, and we are left to infer this.  It’s not hard to guess, but a rhetorically powerful sentence doesn’t leave its main point up to guesswork for the reader.   Choice (D) is incorrect.

This leaves choice (A).  Choice (A) may seem wordy, because it employs the emphatic structure of the empty “it.”  This structure is justified by the subject, and this choice makes all the logically relationships explicitly clear.   It is direct and powerful.  Choice (A) is the best answer.

 

 

8) A sentence about the famous Treaty of Utrecht that mentions the Sun King, Louis XIV.  The whole sentence is underlined, so we will go through each choice individually.

(A) This choice is grammatically and logically correct.  This is a promising choice.

(B) This choice commits the famous missing-verb mistake.  The Treaty appears to be the subject, but there is no bonafide verb in the entire sentence.  Choice (B) is incorrect.

(C) This choice makes the rhetorically questionable move of making the bland phrase “series of documents” the main subject, while relegating the actual name of the treaty to a parenthetical mention.  This strangely de-emphasizes the treaty that presumably is the focus of the sentence.  Also, the second half of the sentence changes the logical relationship of Louis XIV’s actions.  Choice (C) is incorrect.

(D) The prompt tells us one effect of the Treaty of Utrecht.  Was this the only effect of this treaty?  That’s unclear and outside the scope of the sentence, but the prompt leaves open the possibility that this treaty had many effects and it is discussing only one of these effects.  Choice (D) implies that the effect discussed in the sentence is the only effect of the treaty, and this a change in meaning.  Choice (D) is incorrect.

(E) The first half of the sentence focuses on one of the most powerful actors of 17th century Europe, Louis XIV, making him the subject.  All well and good, but now the Treaty of Utrecht is relegated to a small detail role in the sentence, so the focus is now completely different.  Also, the ending of this is awkward and slightly different in meaning from the prompt.  Choice (E) is incorrect.

The only possible answer is choice (A).

 

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A Guide to the Harvard Business School Essay 2016 [#permalink]

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FROM Magoosh Blog: A Guide to the Harvard Business School Essay 2016
This post is most relevant to folks applying to Harvard Business School in 2016, but in many ways, it could be helpful for folks considering application essays for many business schools.  This year, the question on the application for the class of 2019 is simply the open ended question: “As we review your application, what more would you like us to know as we consider your candidacy for the Harvard Business School MBA program?” The website adds the parenthetical advice: “There is no word limit for this question.  We think you know what guidance we’re going to give here. Don’t overthink, overcraft and overwrite. Just answer the question in clear language that those of us who don’t know your world can understand.” 

Like the other Harvard essay questions in recent years, this is astonishingly open-ended: as Bob Dylan said, “but for the sky there are no fences facin’.”  The caveat of using clear and simple language is particularly striking: the Sermon on the Mount, Sojourner Truth’s spontaneous address at an 1851 Woman’s Convention, and Dr. King’s I Have a Dream speech all are examples, in straightforward language that anyone could appreciate, of works that communicate something profound about what it is to be human.  The Gettysburg Address, a profound political statement, is also a masterpiece of earnest simplicity.  What those four have in common is the gift of capturing, in specific memorable phrases, words that touch us to the core.  That is the standard for which to strive.

What the Harvard Business School essay is not
Think about it.  The folks on the HBS adcom already will know your GPA, your GMAT score, your work experience—all the cut-and-dry aspects of your qualifications.  Keep in mind that, across the spectrum of HBS applicants, a great deal of the cut-and-dry stuff will look similar: impressive GPAs at impressive undergraduate institutions, impressive GMAT scores, impressive recommendations, impressive work experience, etc.   Think about the intelligent folks who work on adcom: they see this slate of impressive data for candidate after candidate.  These folks need something to give them a glimpse into the person behind the data.  If your papers look like those of dozens of other applicants, and there is nothing to make you stand out as special, then they are unlikely to get excited about you in particular.

So don’t use the essay to repeat any of the cut-and-dry information: that would be simply redundant and annoying.  Don’t craft an argument about why you would be particularly impressive, because this could very easily come off as weak and needy.

Think about about ordinary everyday human relationships.  If I approach potential friends with the energy of “Gee, I really want you to like me,” that is likely to be perceived as needy and off-putting.  By contrast, if I am confident in who I am and present myself unapologetically as who I am, that may put off some but it ultimately will garner more allegiance and enthusiasm.  If you can balance unapologetic confidence with heartfelt compassion and sincere vulnerability, that is a combination that will open a great many doors.

If you have faced particular challenges in your life, these might already be present in other parts of your application (perhaps in your recommendations).  If not, you might mention in passing the challenges unique to your situation, simply touch on them, but the whole focus of this essay should be where you are going, not where you have been.

Thoughts on approaching this essay
Here are a few thoughts about how one might approach this essay.  This advice is likely to applicable to many other essays on many other applications.

1) Write from the heart, not from the head: of course, once you have a message, it’s fine to use your head to make sure the grammar is good, etc.  The core message, though, should come straight from your heart.  This is your life: what inspires you? What gets you excited and passionate?  Speak about what inspires you at the deepest level.  Don’t make a head-centered argument.  Think in terms of  your heart, and make it your goal to speak to the hearts of your readers.

2) Focus more on “why” than “what”: a laundry list of what you want to do is not particularly engaging, no matter how impressive the items are.  People connect with why.  Simon Sinek argues that we should “start with why.”  Why do you want to do what you want to do? Why does it matter to you?  Why should it matter to anyone else?  Say more about your vision and your dream than about your plans.

3) Be completely honest and authentic: the folks on HBS adcom want to know who you are.  If you speak in your in full sincerity, they can feel who you are.  If you try to make yourself appear as something other than what you are, in all likelihood this will not come off well.  Make the essay an honest statement of who you are and what you are about.  Nothing is more impressive than the utter sincerity of someone who has absolutely no intention of impressing anyone.

4) Be poetic: it can be hard to communicate one’s feelings, one’s dreams, the language of one’s heart, into words.  Often a well-chosen metaphor is perfect for conveying what one has to say.  In the fourth and fifth paragraphs of the “I Have a Dream” speech, Dr. King uses the metaphor of a bank check to discuss issues of racial justice, and this very plain metaphor became the occasion for powerful statements.  A metaphor can powerfully convey your vision, but you must be careful: anything that sounds cliché will fall flat.  It’s tricky, because sometimes the most brilliant metaphors are just a shade different from cliché.  Please get extensive feedback on any metaphorical statement you choose.

Admittedly, this final recommendation would be more challenging if you don’t already have the habit of reading poetry for enjoyment.  Of course, Bob Dylan, mentioned above, is justifiably called “the poet” of rock music.  One poet I would recommend is David Whyte, who has work extensively with corporations and business people; his work The Heart Aroused: Poetry and the Preservation of Soul in Corporate America may be a particularly germane introduction to poetry for anyone contemplating an MBA, and studying that book may give you access to some of the metaphors that mean the most to you.  If you want to be more daring in your exploration of business and poetry, you might examine the poems of the banker T.S. Eliot or the insurance executive Wallace Stevens.

Blank canvas
In giving you such a wide open prompt, HBS is giving you a blank canvas.  Some people, given a blank canvas, can barely produce stick figures.  Given a blank canvas, Leonardo produced the Lady with an Ermine.  Given a blank canvas, Botticelli produced Primavera.  Given a blank canvas, Van Gogh painted wheat fields.  Every masterpiece began with a blank canvas.  That is precisely your situation in facing this essay.  What masterpiece will you create?

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GMAT Data Sufficiency Geometry Practice Question [#permalink]

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FROM Magoosh Blog: GMAT Data Sufficiency Geometry Practice Question
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1) In quadrilateral ABCD, is angle D ≤ 100 degrees?

Statement #1: AB = BC

Statement #2: angle A = angle B = angle C

 

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2) Point P is a point inside triangle ABC.  Is triangle ABC equilateral?

Statement #1: Point P is equidistant from the three vertices A, B, and C.

Statement #2: Triangle ABC has two different lines of symmetry that pass through point P.

 

3) ABC is an equilateral triangle, and point D is the midpoint of side BC.  A is also a point on circle with radius r = 3.  What is the area of the triangle?

Statement #1: The line that passes through A and D also passes through the center of the circle.

Statement #2: Including point A, the triangle intersects the circle at exactly four points.

 

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4) ABCD is a square, and EFGH is a square, each vertex of which is on a side of ABCD.  What is the ratio of the area of square EFGH to the area of square ABCD?

Statement #1: AE:AB = 4:7

Statement #2: The ratio of the area of triangle AHE to the area of square EFGH is 0.24

 

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5) In the diagram above, the four triangles ABE, CBE, ADE, and CDE are all equal, and CD = 5.  What is the area between the two circles?

Statement #1: AE = 3

Statement #2: angle BEC = 90 degrees

 

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6) In trapezoid JKLM, KL//JM, and JK = LM = 5.  What is the area of this trapezoid?

Statement #1: KL = 10 and JM = 15

Statement #2: angle J = 60 degrees

 

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7) In the diagram above, ADF is a right triangle.  BCED is a square with an area of 12.  What is the area of triangle ADF?

Statement #1: angle DCF = 75 degrees

Statement #2: AB:EF = 3

 

8) FGHJ is a rectangle, such that FJ = 40 and FJ > FG.  Point M is the midpoint of FJ, and a Circle C is constructed such that M is the center and FJ is the diameter.   Circle C intersects the top side of the rectangle, GH, at two separate points.  Point P is located on side GH.  What is the area of triangle FJP?

Statement #1: One of the two intersections of Circle C with side GH is point P, one vertex of the triangle FJP.

Statement #2: One of the two intersections of Circle C with side GH is point R, such that RH = 7

 

9) Points A, B, and C are points on a circle with a radius of 6.  Point D is the midpoint of side AC.  What is the area of triangle ABC?

Statement #1: Segment BD passes through the center of the circle.

Statement #2: Arc AB has a length of 4(pi)

 

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10) In the figure, ABCD is a trapezoid with BC//AD, AB = CE, BE//CG, and angle AEB = 90°.  Point M is the midpoint of side BD.  Point F, not shown, is a vertex on triangle EFG such that EF = FG.  Is point F inside the trapezoid?

Statement #1: BE = EG

Statement #2: FG//CD

Full solutions will come at the end of this article.

 

Geometry on the GMAT Data Sufficiency
Here are two previous blogs on GMAT DS questions about Geometry.

GMAT Data Sufficiency: Congruence Rules

GMAT Geometry: Is It a Square?

One big difference between Geometry on the PS questions and Geometry on the DS questions is that for all the PS questions, unless otherwise noted, you know that all diagrams are drawn as accurately as possible.   That is the written guarantee of the test writers.  By contrast, no guarantee at all accompanies the diagrams on the DS questions.   Consider the following diagram.

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This triangle appears equilateral.  There is no guarantee that it is exactly equilateral, with three exactly equal sides and angles exactly equal to 60 degrees.  If this were diagram given on a PS questions, we would know that the triangle is at least close to equilateral: all the side lengths are close to one another, and the angles are close to 60 degrees.  We would know that much on a PS question.  If this diagram were given on a DS question, then triangle ABC could be absolutely any triangle on the face of the Earth.   It could be a right triangle, or a triangle with a big obtuse angle, or a tall & thin triangle, or a short & wide triangle, or etc.  It could be any triangle at all.  Aside from the bare fact that ABC is some kind of triangle, we can deduce nothing from the diagram on a DS question.  Other than the bare facts of what’s connected to what, you can deduce nothing about lengths, angles, and shapes of figures given on DS questions.  They may be 100% accurate or they may look nothing like the the shape described by the two statements.

Because of this, some DS questions are a real test of your capacity for spatial reasoning and geometric imagination.  Many DS Geometry questions, including ones here, test your capacity to imagine how different the spatial scenario might be.

If this is not a natural gift for you, I strong recommend drawing out shapes on paper.  Even get a ruler, compass, and protractor, and practice constructing specific shapes.  Use straws or some other straight items to construct triangles in which you can adjust the sides and the angles.  Strive to visualize and picture physically every rule of geometry you learn.  By working with shapes you can see, and working with your hands, you will be engaging multiple parts of your brain that will give you a much deeper understanding of geometry.

 

Summary
If the above discussion gave you some insights, you may want to look back at those practice problems before jumping into the explanations below.  If you don’t understand something said in an explanation here, draw it yourself, and explore the different possibilities within the constraints.   The point of geometry is to see.

Image

 

Text Explanations
1) The figure is drawn as a square, but on GMAT DS, there’s no reason to assume the figure is drawn anywhere to scale.

If both statements are true, then the figure could be a square, in which the answer to the prompt question would be “yes,” or it could be this figure:

Image

For this figure, all the conditions are met, and angle D is considerably larger than 100°; thus, the answer to the prompt question is “no.”

We could get either a “yes” or a “no” to the prompt consistent with these conditions, even with both statements put together.

Answer = (E)

 

2) Statement #1: As it turns out, for any triangle of any shape, there is some point that is equidistant from all three vertices: this is center of the circle that passes through all three vertices.

Image

If all three angles of the triangle are acute, then the point is inside the triangle.  If the triangle is a right triangle, then this center is always the midpoint of the hypotenuse.  If the triangle has an obtuse angle, then the center is outside the triangle.  All Statement #1 tells us is that triangle ABD has three acute angles.  Beyond that, we know nothing.  Statement #1, alone and by itself, is not sufficient.

Statement #2: A triangle that has a line of symmetry is isosceles.  Let’s say that one line of symmetry goes through vertex A and point P.  This would mean that AB = AC and that angle B = angle C.  Now, let’s say that another line of symmetry goes through vertex B and point B.  This would mean that AB = BC and angle A = angle C.  Putting those together, we get three equal angles and three equal sides: an equilateral triangle.  If a triangle has two separate lines of symmetry, it must be an equilateral triangle.  We can give a definitive “yes” to the prompt question on the basis of this statement.   Statement #2, alone and by itself, is sufficient.

Answer = (B)

 

3)  Statement #1 tells us that the center of the circle is on the line of symmetry of the triangle through point A, but the triangle could be any size.  In the diagram below, this line of symmetry is blue, and triangles of four different sizes are shown.

Image

There actually would be an infinite number of possible triangle sizes on the basis of this statement alone.  This statement is wildly insufficient.

Forget about Statement #1.  With Statement #2 alone, a variety of off-center triangles with four intersection points are possible:

Image

Notice AB is a chord of the circle as well as a side of the triangle.  This chord could be a medium length chord or anything up to the full diameter, and different sides of the triangle would result in different areas.  We still cannot give a definitive answer to the prompt question.  This statement, alone and by itself, is insufficient.

Combined statements.  If the center of the circle is on the line of symmetry of the triangle, then this places significant constraints on the number of intersections.  For tiny triangles, they would simply intersect at point A and not reach the circle on the other side: one point of intersection, so this doesn’t work.

Image

Larger triangles would touch the circle in three places, at the three vertices: this also doesn’t work.

Image

Slightly larger, and those two vertices at B and C would “poke out” of the triangle, producing five points of intersection: Point A plus four other points.

Image

The only way we will get exactly four points is when the sides get long enough and the side BC drops low enough that it is tangent to the circle.

Image

The altitude of this triangle, AD is exactly equal to the diameter.  We could use the ratios of the 30-60-90 triangle to figure out the sides, and thus figure out the area.  If the sides get any longer, then side BC would break contact with the circle, and there would be only three points of intersection.  This triangle, with the point of tangency at D, is the only triangle on this line of symmetry that has exactly four intersection points, and we can compute its area.

The combined statements allow us to give a numerical answer to the prompt question, so together, the statements are sufficient.

Answer = (C)

 

4) Statement #1: since we care only about ratios, we can set any lengths that are convenient.  Let AE = 3 and AB = 7: then BE = 3.  The figure is symmetrical on all four sides, so, for example, AH = 3.  This means AEH is a right triangle with legs of 3 and 4—that is, a 3-4-5 triangle!  The hypotenuse HE = 5.  That’s the side of the smaller square, and 7 is the side of the larger square.  The ratio of areas is 25/49.   This statement leads directly to a numerical answer to the prompt question.   This statement, alone and by itself, is sufficient.

Now, forget all about statement #1.

Statement #2: triangle to small square = 0.24 = 24/100 = 6/25.  Let’s say that the central square has an area of 25 and one triangle has an area of 6.  This means that four triangles together would have an area of 24.  The big square equals the central square plus four triangles: 24 + 25 = 49.  The ratio of the two squares = 25/49.  This statement also leads directly to a numerical answer to the prompt question.   This statement, alone and by itself, is sufficient.

Each statement sufficient on its own.  Answer = (D)

 

5) Statement #1: If AE = 3, then it must be true that EC = 3, because the triangles are all equal.  Also, AB = BC = CD = AD = 5.  Because the four angles meeting at point E are all equal, it must be true that each one equals 90 degrees.  Thus, we have four right triangles, and each one has a leg of 3 and an hypotenuse of 5.  Thus, each must be a 3-4-5 triangle.  This allows us to see that the radius of the smaller circle is EC = 3 and the radius of the larger circle is BE = 4.  From these, we could figure out the areas and then subtract these areas to find the area between them.   This statement allows us to arrive at a numerical answer to the prompt question.  Statement #1, alone and by itself, is sufficient.

Statement #2: This statement tells us something we already could figure out from the prompt information.  Technically, this statement is tautological.  A tautological statement is one that contains no new information, nothing new that we couldn’t figure out on our own; examples of tautologies are “My favorite flavor of ice cream is the flavor I like most” or “Today is the day after yesterday.”  Like those statements, Statement #2 adds nothing to our understanding.   Statement #2, alone and by itself, is not sufficient.

Answer = (A)

 

6) This is question that demands visual insight.

Statement #1:  Think about these lengths.  The top, KL is twice the length of the slanted sides, and the bottom, JM, is three times the length.  This means that we could build this trapezoid from five equilateral triangles.

Image

With other combinations of four lengths, we would be able to get different quadrilaterals resulting (e.g. changing the tilt of a rhombus).  With these lengths (5, 10, 5, 15), there is no other quadrilateral possible.  (Try this with physical items with lengths in the ratio 1:2:1:3 to see for yourself.)  Thus, we know all the angles.  We know that each equilateral has side of 5, so we could figure out the area of each equilateral, then multiply by five.   Thus, we can find the area on the bases of this statement alone.  Statement #1, alone and by itself, is sufficient.

Statement #2:  If we know just this, then the shape could have any width.  It could be relative narrow or a mile-wide.  We cannot determine a unique area on the basis of this statement alone.  Statement #2, alone and by itself, is not sufficient.

Answer = (A)

 

7) We know the area of the square, so the side of the square is

Image

Thus, we know the length of the vertical leg, CE, in right triangle CEF, and we know the horizontal leg, BC, in right triangle ABC.  Furthermore, these two triangles must be similar to teach other and similar to the larger triangle, ADF, because all the angles are the same.

Statement #1: We know triangle CDE is a half a square, so it’s a 45-45-90 triangle.  Angle DCE = 45 degrees.  Well,

(Angle ECF) = (Angle DCF) – (Angle DCE) = 75 – 45 = 30 degrees

This means that CEF is a 30-60-90 triangles, and so is triangle ABC because they are similar.   In each, we know the length of one side, so we could find the other sides and solve for the areas.  Thus, we could find the area of the entire triangle ADF.  This statement leads directly to a numerical answer to the prompt question.  Statement #1, alone and by itself, is sufficient.

Statement #1: This is interesting.  We know that triangles ABC and CEF are similar, so they are proportional.  Let AB:BC = r.  Then CE:EF = r as well.

Image

Now, notice that both BC and CE are sides of the square.  Let BC = CE = s.

Image

Now, multiply those two fractions together, and the s terms will cancel.

Image

This the ratio of the longer leg to the shorter leg in the 30:60:90 triangle.  We know the sides of the square, so we can find all the lengths in triangles ABC and CEF, which would allow us to find all the areas.  Thus, we could find the area of the entire triangle ADF.  This statement leads directly to a numerical answer to the prompt question.  Statement #2, alone and by itself, is sufficient.

Each statement is sufficient on its own.  Answer = (D)

 

8) We know the diameter of the circle is FJ = 40, so its radius is r = 20.  FJ = 40 is also the base of the triangle in question.  We need the height of the triangle in order to find its area.

Statement #1:  We know point P is one of the two points where the circle intersects side GH, the top of the rectangle.  We still don’t know how tall the rectangle is.  We know the height must be less than 20, so that the circle can intersect it, but we certainly don’t know the exact height.

Image

Without an exact height, we cannot compute an exact area.  Statement #1, alone and by itself, is not sufficient.

Statement #2: Construct Point Q, the midpoint of GH, and draw in segments MQ and MR.  MQ joins midpoints of opposite sides of a rectangle, so this would be perpendicular to both FJ and GH.

Image

We know that MR is a radius, so it has a length of 20.  We know that QH is half the length of GH, so QH = 20.  We know that RH = 7.  Notice

QR + RH = QH

QR = QH – RH = 20 – 7 = 13

Now, look at right triangle MQR.  We know the hypotenuse MR = 20.  We know the horizontal leg QR = 13.  We could use that most extraordinary mathematical theorem, the Pythagorean Theorem, to find the length of QM.  On GMAT Data Sufficiency, we don’t have to carry out the actual calculation: it results in an ugly radical expression anyway.  It’s enough to know that we could find the numerical value of QM, the height of the rectangle.

We don’t know the exact position of point P, but it’s somewhere on GH, and every point on GH has the same height above FJ, so this height would be equal to the height of the triangle.  Thus, we could find the height of the triangle, and therefore the area.  On the basis of this statement, we could give a numerical response to the prompt question.  Statement #2, alone and by itself, is sufficient.

Answer = (B)

 

9) Statement #1: This one guarantees that BD is a line of symmetry in the diagram, so triangle ABC would have to be isosceles, but it could be any one of a number of a different sizes & shapes.

Image

In all these examples, AB = BC and (angle A) = (angle C).  The triangle could be equilateral, but it doesn’t have to be.  These three examples have different areas, so this statement, by itself does not guarantee that we could calculate an exact area.   Statement #1, alone and by itself, is not sufficient.

Now, forget all about statement #1.

Statement #2: We know that the radius is r = 6, so

Image

Thus, we know that arc AB is 1/3 of the entire circumference.  Therefore, it must occupy an angle of 1/3 of 360 degrees: arc AB must occupy 120 degrees.

In an equilateral triangle, all three angles would be 60 degrees and all three arcs would be 120 degrees.  Here, all we know is that one arc, AB, is 120 degrees, and other two arcs could be other values.  Thus, angle C must be 60 degrees, but other other angles can be other values.

Image

In all three of those diagrams, AB is a 120 degree arc and angle C is 60 degrees.  The triangle could be equilateral, but it doesn’t have to be.  Statement #2, alone and by itself, is not sufficient.

Now combine the statements.  From the first statement, we know that AB = BC and (angle A) = (angle C).  From the second statement, we know that (angle C) = 60 degrees.  Well, that would mean that (angle A) = 60 degrees as well, and that leaves exactly 60 degrees for angle B.  If we have three 60 degree angles, we know that ABC is equilateral.   If we know the radius of a circle, then we can calculate the area of an equilateral triangle with its three vertices on the circle (this would involve subdividing the equilateral into six 30-60-90 triangles).

Image

With the combined information of both statements, we can find a definitive answer for the prompt question.  Together, the statements are sufficient.

Answer = (C)

 

10) Start with what we know from the prompt.  We know BCGE is a rectangle with two parallel vertical sides that are perpendicular to two parallel horizontal sides.

We know that ABE and CGD are right triangles with the same length vertical legs and the same length hypotenuses, so by the Pythagorean theorem, the third sides must be equal, AE = DG, and the two triangles are equal in every respect.

We know that entirely figure is symmetrical around a vertical line down the middle.  The trapezoid is entirely symmetrical, and isosceles triangle EFG is also symmetrical.  Suppose we constructed the midpoint of EG and called it Q.  Then, line MQ would be the symmetry line of both the trapezoid and the isosceles triangle.  This line MQ would be parallel to BE and CG, and it would be perpendicular to BC and EG.   If we extended MQ above and below the trapezoid, we would be guaranteed that point F would lie somewhere on this line.

For this problem, I am going to jump ahead to the combined statements.  Statement #1 tells us that BCGE is a square.  Statement #2 tells that the sides of the trapezoid are parallel to the sides of the isosceles triangle (by symmetry, the parallelism must be true on both the right and the left side).   Even with all this information, we cannot give a definitive answer to the prompt question.

You see, the missing piece are the lengths of AE and DG.  By the symmetry of the diagram, we know AE = DG, but we don’t know how this size compares to BM = MC.  In the diagram, it appears that DG < MC, but because this is a GMAT DS diagram, we can’t believe sizes on the diagram.

Image

If DG < MC, then point F will be above M, outside of the trapezoid, as seen in the diagram on the left.  If DG = MC, then point P will coincide with point M.  If DG > MC, then point F will be below point M, inside the trapezoid.

Because we don’t know how the AE = DG length compares to the BM = MC length, we don’t know where point F falls, and we can’t give a definitive answer to the prompt question.  Even combined, the statements are insufficient.

Answer = (E)

 

The post GMAT Data Sufficiency Geometry Practice Question appeared first on Magoosh GMAT Blog.
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GMAT Data Sufficiency Geometry Practice Questions [#permalink]

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New post 24 May 2016, 11:02
FROM Magoosh Blog: GMAT Data Sufficiency Geometry Practice Questions
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1) In quadrilateral ABCD, is angle D ≤ 100 degrees?

Statement #1: AB = BC

Statement #2: angle A = angle B = angle C

 

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2) Point P is a point inside triangle ABC.  Is triangle ABC equilateral?

Statement #1: Point P is equidistant from the three vertices A, B, and C.

Statement #2: Triangle ABC has two different lines of symmetry that pass through point P.

 

3) ABC is an equilateral triangle, and point D is the midpoint of side BC.  A is also a point on circle with radius r = 3.  What is the area of the triangle?

Statement #1: The line that passes through A and D also passes through the center of the circle.

Statement #2: Including point A, the triangle intersects the circle at exactly four points.

 

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4) ABCD is a square, and EFGH is a square, each vertex of which is on a side of ABCD.  What is the ratio of the area of square EFGH to the area of square ABCD?

Statement #1: AE:AB = 4:7

Statement #2: The ratio of the area of triangle AHE to the area of square EFGH is 0.24

 

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5) In the diagram above, the four triangles ABE, CBE, ADE, and CDE are all equal, and CD = 5.  What is the area between the two circles?

Statement #1: AE = 3

Statement #2: angle BEC = 90 degrees

 

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6) In trapezoid JKLM, KL//JM, and JK = LM = 5.  What is the area of this trapezoid?

Statement #1: KL = 10 and JM = 15

Statement #2: angle J = 60 degrees

 

Image

7) In the diagram above, ADF is a right triangle.  BCED is a square with an area of 12.  What is the area of triangle ADF?

Statement #1: angle DCF = 75 degrees

Statement #2: AB:EF = 3

 

8) FGHJ is a rectangle, such that FJ = 40 and FJ > FG.  Point M is the midpoint of FJ, and a Circle C is constructed such that M is the center and FJ is the diameter.   Circle C intersects the top side of the rectangle, GH, at two separate points.  Point P is located on side GH.  What is the area of triangle FJP?

Statement #1: One of the two intersections of Circle C with side GH is point P, one vertex of the triangle FJP.

Statement #2: One of the two intersections of Circle C with side GH is point R, such that RH = 7

 

9) Points A, B, and C are points on a circle with a radius of 6.  Point D is the midpoint of side AC.  What is the area of triangle ABC?

Statement #1: Segment BD passes through the center of the circle.

Statement #2: Arc AB has a length of 4(pi)

 

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10) In the figure, ABCD is a trapezoid with BC//AD, AB = CE, BE//CG, and angle AEB = 90°.  Point M is the midpoint of side BD.  Point F, not shown, is a vertex on triangle EFG such that EF = FG.  Is point F inside the trapezoid?

Statement #1: BE = EG

Statement #2: FG//CD

Full solutions will come at the end of this article.

 

Geometry on the GMAT Data Sufficiency
Here are two previous blogs on GMAT DS questions about Geometry.

GMAT Data Sufficiency: Congruence Rules

GMAT Geometry: Is It a Square?

One big difference between Geometry on the PS questions and Geometry on the DS questions is that for all the PS questions, unless otherwise noted, you know that all diagrams are drawn as accurately as possible.   That is the written guarantee of the test writers.  By contrast, no guarantee at all accompanies the diagrams on the DS questions.   Consider the following diagram.

Image

This triangle appears equilateral.  There is no guarantee that it is exactly equilateral, with three exactly equal sides and angles exactly equal to 60 degrees.  If this were diagram given on a PS questions, we would know that the triangle is at least close to equilateral: all the side lengths are close to one another, and the angles are close to 60 degrees.  We would know that much on a PS question.  If this diagram were given on a DS question, then triangle ABC could be absolutely any triangle on the face of the Earth.   It could be a right triangle, or a triangle with a big obtuse angle, or a tall & thin triangle, or a short & wide triangle, or etc.  It could be any triangle at all.  Aside from the bare fact that ABC is some kind of triangle, we can deduce nothing from the diagram on a DS question.  Other than the bare facts of what’s connected to what, you can deduce nothing about lengths, angles, and shapes of figures given on DS questions.  They may be 100% accurate or they may look nothing like the the shape described by the two statements.

Because of this, some DS questions are a real test of your capacity for spatial reasoning and geometric imagination.  Many DS Geometry questions, including ones here, test your capacity to imagine how different the spatial scenario might be.

If this is not a natural gift for you, I strong recommend drawing out shapes on paper.  Even get a ruler, compass, and protractor, and practice constructing specific shapes.  Use straws or some other straight items to construct triangles in which you can adjust the sides and the angles.  Strive to visualize and picture physically every rule of geometry you learn.  By working with shapes you can see, and working with your hands, you will be engaging multiple parts of your brain that will give you a much deeper understanding of geometry.

 

Summary
If the above discussion gave you some insights, you may want to look back at those practice problems before jumping into the explanations below.  If you don’t understand something said in an explanation here, draw it yourself, and explore the different possibilities within the constraints.   The point of geometry is to see.

Image

 

Text Explanations
1) The figure is drawn as a square, but on GMAT DS, there’s no reason to assume the figure is drawn anywhere to scale.

If both statements are true, then the figure could be a square, in which the answer to the prompt question would be “yes,” or it could be this figure:

Image

For this figure, all the conditions are met, and angle D is considerably larger than 100°; thus, the answer to the prompt question is “no.”

We could get either a “yes” or a “no” to the prompt consistent with these conditions, even with both statements put together.

Answer = (E)

 

2) Statement #1: As it turns out, for any triangle of any shape, there is some point that is equidistant from all three vertices: this is center of the circle that passes through all three vertices.

Image

If all three angles of the triangle are acute, then the point is inside the triangle.  If the triangle is a right triangle, then this center is always the midpoint of the hypotenuse.  If the triangle has an obtuse angle, then the center is outside the triangle.  All Statement #1 tells us is that triangle ABD has three acute angles.  Beyond that, we know nothing.  Statement #1, alone and by itself, is not sufficient.

Statement #2: A triangle that has a line of symmetry is isosceles.  Let’s say that one line of symmetry goes through vertex A and point P.  This would mean that AB = AC and that angle B = angle C.  Now, let’s say that another line of symmetry goes through vertex B and point B.  This would mean that AB = BC and angle A = angle C.  Putting those together, we get three equal angles and three equal sides: an equilateral triangle.  If a triangle has two separate lines of symmetry, it must be an equilateral triangle.  We can give a definitive “yes” to the prompt question on the basis of this statement.   Statement #2, alone and by itself, is sufficient.

Answer = (B)

 

3)  Statement #1 tells us that the center of the circle is on the line of symmetry of the triangle through point A, but the triangle could be any size.  In the diagram below, this line of symmetry is blue, and triangles of four different sizes are shown.

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There actually would be an infinite number of possible triangle sizes on the basis of this statement alone.  This statement is wildly insufficient.

Forget about Statement #1.  With Statement #2 alone, a variety of off-center triangles with four intersection points are possible:

Image

Notice AB is a chord of the circle as well as a side of the triangle.  This chord could be a medium length chord or anything up to the full diameter, and different sides of the triangle would result in different areas.  We still cannot give a definitive answer to the prompt question.  This statement, alone and by itself, is insufficient.

Combined statements.  If the center of the circle is on the line of symmetry of the triangle, then this places significant constraints on the number of intersections.  For tiny triangles, they would simply intersect at point A and not reach the circle on the other side: one point of intersection, so this doesn’t work.

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Larger triangles would touch the circle in three places, at the three vertices: this also doesn’t work.

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Slightly larger, and those two vertices at B and C would “poke out” of the triangle, producing five points of intersection: Point A plus four other points.

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The only way we will get exactly four points is when the sides get long enough and the side BC drops low enough that it is tangent to the circle.

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The altitude of this triangle, AD is exactly equal to the diameter.  We could use the ratios of the 30-60-90 triangle to figure out the sides, and thus figure out the area.  If the sides get any longer, then side BC would break contact with the circle, and there would be only three points of intersection.  This triangle, with the point of tangency at D, is the only triangle on this line of symmetry that has exactly four intersection points, and we can compute its area.

The combined statements allow us to give a numerical answer to the prompt question, so together, the statements are sufficient.

Answer = (C)

 

4) Statement #1: since we care only about ratios, we can set any lengths that are convenient.  Let AE = 3 and AB = 7: then BE = 3.  The figure is symmetrical on all four sides, so, for example, AH = 3.  This means AEH is a right triangle with legs of 3 and 4—that is, a 3-4-5 triangle!  The hypotenuse HE = 5.  That’s the side of the smaller square, and 7 is the side of the larger square.  The ratio of areas is 25/49.   This statement leads directly to a numerical answer to the prompt question.   This statement, alone and by itself, is sufficient.

Now, forget all about statement #1.

Statement #2: triangle to small square = 0.24 = 24/100 = 6/25.  Let’s say that the central square has an area of 25 and one triangle has an area of 6.  This means that four triangles together would have an area of 24.  The big square equals the central square plus four triangles: 24 + 25 = 49.  The ratio of the two squares = 25/49.  This statement also leads directly to a numerical answer to the prompt question.   This statement, alone and by itself, is sufficient.

Each statement sufficient on its own.  Answer = (D)

 

5) Statement #1: If AE = 3, then it must be true that EC = 3, because the triangles are all equal.  Also, AB = BC = CD = AD = 5.  Because the four angles meeting at point E are all equal, it must be true that each one equals 90 degrees.  Thus, we have four right triangles, and each one has a leg of 3 and an hypotenuse of 5.  Thus, each must be a 3-4-5 triangle.  This allows us to see that the radius of the smaller circle is EC = 3 and the radius of the larger circle is BE = 4.  From these, we could figure out the areas and then subtract these areas to find the area between them.   This statement allows us to arrive at a numerical answer to the prompt question.  Statement #1, alone and by itself, is sufficient.

Statement #2: This statement tells us something we already could figure out from the prompt information.  Technically, this statement is tautological.  A tautological statement is one that contains no new information, nothing new that we couldn’t figure out on our own; examples of tautologies are “My favorite flavor of ice cream is the flavor I like most” or “Today is the day after yesterday.”  Like those statements, Statement #2 adds nothing to our understanding.   Statement #2, alone and by itself, is not sufficient.

Answer = (A)

 

6) This is question that demands visual insight.

Statement #1:  Think about these lengths.  The top, KL is twice the length of the slanted sides, and the bottom, JM, is three times the length.  This means that we could build this trapezoid from five equilateral triangles.

Image

With other combinations of four lengths, we would be able to get different quadrilaterals resulting (e.g. changing the tilt of a rhombus).  With these lengths (5, 10, 5, 15), there is no other quadrilateral possible.  (Try this with physical items with lengths in the ratio 1:2:1:3 to see for yourself.)  Thus, we know all the angles.  We know that each equilateral has side of 5, so we could figure out the area of each equilateral, then multiply by five.   Thus, we can find the area on the bases of this statement alone.  Statement #1, alone and by itself, is sufficient.

Statement #2:  If we know just this, then the shape could have any width.  It could be relative narrow or a mile-wide.  We cannot determine a unique area on the basis of this statement alone.  Statement #2, alone and by itself, is not sufficient.

Answer = (A)

 

7) We know the area of the square, so the side of the square is

Image

Thus, we know the length of the vertical leg, CE, in right triangle CEF, and we know the horizontal leg, BC, in right triangle ABC.  Furthermore, these two triangles must be similar to teach other and similar to the larger triangle, ADF, because all the angles are the same.

Statement #1: We know triangle CDE is a half a square, so it’s a 45-45-90 triangle.  Angle DCE = 45 degrees.  Well,

(Angle ECF) = (Angle DCF) – (Angle DCE) = 75 – 45 = 30 degrees

This means that CEF is a 30-60-90 triangles, and so is triangle ABC because they are similar.   In each, we know the length of one side, so we could find the other sides and solve for the areas.  Thus, we could find the area of the entire triangle ADF.  This statement leads directly to a numerical answer to the prompt question.  Statement #1, alone and by itself, is sufficient.

Statement #1: This is interesting.  We know that triangles ABC and CEF are similar, so they are proportional.  Let AB:BC = r.  Then CE:EF = r as well.

Image

Now, notice that both BC and CE are sides of the square.  Let BC = CE = s.

Image

Now, multiply those two fractions together, and the s terms will cancel.

Image

This the ratio of the longer leg to the shorter leg in the 30:60:90 triangle.  We know the sides of the square, so we can find all the lengths in triangles ABC and CEF, which would allow us to find all the areas.  Thus, we could find the area of the entire triangle ADF.  This statement leads directly to a numerical answer to the prompt question.  Statement #2, alone and by itself, is sufficient.

Each statement is sufficient on its own.  Answer = (D)

 

8) We know the diameter of the circle is FJ = 40, so its radius is r = 20.  FJ = 40 is also the base of the triangle in question.  We need the height of the triangle in order to find its area.

Statement #1:  We know point P is one of the two points where the circle intersects side GH, the top of the rectangle.  We still don’t know how tall the rectangle is.  We know the height must be less than 20, so that the circle can intersect it, but we certainly don’t know the exact height.

Image

Without an exact height, we cannot compute an exact area.  Statement #1, alone and by itself, is not sufficient.

Statement #2: Construct Point Q, the midpoint of GH, and draw in segments MQ and MR.  MQ joins midpoints of opposite sides of a rectangle, so this would be perpendicular to both FJ and GH.

Image

We know that MR is a radius, so it has a length of 20.  We know that QH is half the length of GH, so QH = 20.  We know that RH = 7.  Notice

QR + RH = QH

QR = QH – RH = 20 – 7 = 13

Now, look at right triangle MQR.  We know the hypotenuse MR = 20.  We know the horizontal leg QR = 13.  We could use that most extraordinary mathematical theorem, the Pythagorean Theorem, to find the length of QM.  On GMAT Data Sufficiency, we don’t have to carry out the actual calculation: it results in an ugly radical expression anyway.  It’s enough to know that we could find the numerical value of QM, the height of the rectangle.

We don’t know the exact position of point P, but it’s somewhere on GH, and every point on GH has the same height above FJ, so this height would be equal to the height of the triangle.  Thus, we could find the height of the triangle, and therefore the area.  On the basis of this statement, we could give a numerical response to the prompt question.  Statement #2, alone and by itself, is sufficient.

Answer = (B)

 

9) Statement #1: This one guarantees that BD is a line of symmetry in the diagram, so triangle ABC would have to be isosceles, but it could be any one of a number of a different sizes & shapes.

Image

In all these examples, AB = BC and (angle A) = (angle C).  The triangle could be equilateral, but it doesn’t have to be.  These three examples have different areas, so this statement, by itself does not guarantee that we could calculate an exact area.   Statement #1, alone and by itself, is not sufficient.

Now, forget all about statement #1.

Statement #2: We know that the radius is r = 6, so

Image

Thus, we know that arc AB is 1/3 of the entire circumference.  Therefore, it must occupy an angle of 1/3 of 360 degrees: arc AB must occupy 120 degrees.

In an equilateral triangle, all three angles would be 60 degrees and all three arcs would be 120 degrees.  Here, all we know is that one arc, AB, is 120 degrees, and other two arcs could be other values.  Thus, angle C must be 60 degrees, but other other angles can be other values.

Image

In all three of those diagrams, AB is a 120 degree arc and angle C is 60 degrees.  The triangle could be equilateral, but it doesn’t have to be.  Statement #2, alone and by itself, is not sufficient.

Now combine the statements.  From the first statement, we know that AB = BC and (angle A) = (angle C).  From the second statement, we know that (angle C) = 60 degrees.  Well, that would mean that (angle A) = 60 degrees as well, and that leaves exactly 60 degrees for angle B.  If we have three 60 degree angles, we know that ABC is equilateral.   If we know the radius of a circle, then we can calculate the area of an equilateral triangle with its three vertices on the circle (this would involve subdividing the equilateral into six 30-60-90 triangles).

Image

With the combined information of both statements, we can find a definitive answer for the prompt question.  Together, the statements are sufficient.

Answer = (C)

 

10) Start with what we know from the prompt.  We know BCGE is a rectangle with two parallel vertical sides that are perpendicular to two parallel horizontal sides.

We know that ABE and CGD are right triangles with the same length vertical legs and the same length hypotenuses, so by the Pythagorean theorem, the third sides must be equal, AE = DG, and the two triangles are equal in every respect.

We know that entirely figure is symmetrical around a vertical line down the middle.  The trapezoid is entirely symmetrical, and isosceles triangle EFG is also symmetrical.  Suppose we constructed the midpoint of EG and called it Q.  Then, line MQ would be the symmetry line of both the trapezoid and the isosceles triangle.  This line MQ would be parallel to BE and CG, and it would be perpendicular to BC and EG.   If we extended MQ above and below the trapezoid, we would be guaranteed that point F would lie somewhere on this line.

For this problem, I am going to jump ahead to the combined statements.  Statement #1 tells us that BCGE is a square.  Statement #2 tells that the sides of the trapezoid are parallel to the sides of the isosceles triangle (by symmetry, the parallelism must be true on both the right and the left side).   Even with all this information, we cannot give a definitive answer to the prompt question.

You see, the missing piece are the lengths of AE and DG.  By the symmetry of the diagram, we know AE = DG, but we don’t know how this size compares to BM = MC.  In the diagram, it appears that DG < MC, but because this is a GMAT DS diagram, we can’t believe sizes on the diagram.

Image

If DG < MC, then point F will be above M, outside of the trapezoid, as seen in the diagram on the left.  If DG = MC, then point P will coincide with point M.  If DG > MC, then point F will be below point M, inside the trapezoid.

Because we don’t know how the AE = DG length compares to the BM = MC length, we don’t know where point F falls, and we can’t give a definitive answer to the prompt question.  Even combined, the statements are insufficient.

Answer = (E)

 

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GMAT Tuesday: Common Flaws in AWA – Sampling Error [#permalink]

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New post 24 May 2016, 14:01
FROM Magoosh Blog: GMAT Tuesday: Common Flaws in AWA – Sampling Error
When attacking the argument for the writing section of the GMAT, it’s important to be versed in the many common errors that pop up. This week we look at sampling errors.



For access to the argument that I mention in the video, and all the other possible arguments, click here to download the PDF from mba.com.

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How To Determine Your “Best Fit” MBA Program [#permalink]

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New post 01 Jun 2016, 15:01
FROM Magoosh Blog: How To Determine Your “Best Fit” MBA Program
If I had a dollar for every time an MBA applicant reached out and asked us which MBA programs are the best “fit” for him/her, I wouldn’t be writing this blog post right now. I’d be too busy driving around in my Tesla, counting the gold bars on the passenger seat.

That, followed in a close second by “what are my chances at School X” and “wow, why are you so awesome?!” is the most common question we get. And it makes sense, of course. You’re about to give up 2 years of your life (and a large sum of money) on your MBA; you want to make sure you’re going to get the best possible return on your investment.

The good news is: the answer to that question is a lot easier than most applicants think. And here’s how you get to it:

    1. What is the best possible school you can get into?
    2. Go to that school.
Yup. It really is that simple. I know, I know – there’s a lot of noise out there surrounding this very topic. People talking about a school’s location, teaching methods, “specialty”, scholarships, etc.

But between you and me, when it comes down to it, none of that stuff really matters in the long run. When you break b-school down to its core value – your potential for future success – the only thing that really matters is going to the best school you can get into. And here’s why:

Brand Name Matters:
Whether it should is a different story. But it does. When a hiring manager or VC guy sees “Stanford” or “Yale” or “Haas” on your resume, it tells them something. And that something is that you must be pretty awesome if you made it into one of those highly selective programs. That brand speaks for itself, and gives you instant credibility.

The people around you matter:
As experienced men and women in the business world, you know by now that the best path to success lies in the team and not the idea. There are TONS of examples out there that prove that. So, naturally, you want to surround yourself with the brightest people you can. Not only because they could be the foundation of a very successful future venture; but because they are going to inspire you and challenge you throughout

business school, helping you grow into a stronger leader when you go back into the workforce.

The extended network matters:
All those smart people in your classes? And all the smart people who took those same classes before you? They’re all going to be out there in the real world when you graduate, in all sorts of companies and roles. And that makes for a very powerful network that can open up a lot of doors for you when you, ya know, need some doors opened.

Of course, “the best school” looks different for everyone. Every applicant has a different profile, different experience, different stats. Find out if your GMAT stacks up for top programs. For some, it is HBS. For others it is Duke. For others it is Yale. Or Olin. Or Anderson. But whatever it is for you, go there. Don’t worry about going to a “marketing program” if you are a marketing guy, or a “real estate program” if you’re a real estate guy. Don’t let scholarship money (or, as we like to call it, a bribe) sway you. This is a long-term play that should impact you for the rest of your career, so you have to think beyond the 2 years you will spend in the classroom. Think about what happens when you graduate.

Just go to the best school you can get into. Period.

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GMAT Tuesday: Must Know Idioms #17 [#permalink]

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New post 07 Jun 2016, 12:01
FROM Magoosh Blog: GMAT Tuesday: Must Know Idioms #17
Can you believe there are now 17 videos about idioms? I can’t! I am amazed by all the idioms out there!

This week, you will learn idiomatic expressions involving years, different, capable, and argue.



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GMAT Diagnostic Test Recommendations [#permalink]

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New post 16 Jun 2016, 17:01
FROM Magoosh Blog: GMAT Diagnostic Test Recommendations
This blog article is to make study recommendations to folks who took the Magoosh GMAT Diagnostic Test.  For folks who took both the Quant Diagnostic and the Verbal Diagnostic, the recommendations here will fall into four buckets, according to your scores on the two diagnostic tests.

1) Group 1: Quant score 1-6; Verbal Score 1-6

2) Group 2: Quant score 1-6; Verbal Score 7-10

3) Group 3: Quant score 7-10; Verbal Score 1-6

4) Group 4: Quant score 7-10; Verbal Score 7-10

If you took only one of the two diagnostic tests, probably you have a reasonably good sense of your skill level in the other area, so that should make it easy to figure out which “bucket” best describes where you fit.

If you feel that, for whatever reason, one section or another of the Magoosh GMAT Diagnostic Test did not accurately capture your skills, then feel free to explore the group that you feel represents you the best.  It’s always a tricky thing to balance the well-deserved confidence in one’s own strengths with a grounded sense of humility about what one still has to learn.  Remember that few people have ever harmed themselves by being overly conscientious.   Trust your intuition to follow the recommendations that work best for you.

In each “bucket,” we recommend a different three-month plan.  Three-months is a good solid time that allows for ample improvement in one’s GMAT performance.  If you have more time, you might look at our six-month plan.  If you have less time, look at our one-month plan, but if you can, incorporate some of the materials & recommendations from the relevant three-month plan.

Group #1: Quant Score 1-6; Verbal Score 1-6
Many folks preparing for the GMAT will fall into this group, including most people who are at the very beginning stages of their studying, and that’s perfectly fine.  Yes, this is the “lowest” of the four groups, but this doesn’t NOT mean you are starting with any kind of disadvantage.  In fact, an extremely intelligent student might choose to start with the advice in this section as a gesture of tremendous conscientiousness; from a pedagogical view point, this would be an admirable choice.   I will emphasize, once again, that it is quite possible to start with these recommendations and get a score in the high 700’s on the GMAT.  Again, it all depends on your commitment to excellence.

1) This is the recommended 3-month study plan.  This plan recommends several study resources that you will find helpful.

2) Use the GMAT Math Flashcards = drill these until you know them all

3) Use the GMAT Idiom Flashcards = drill these until you know them all

4) Your results suggest that you need to learn material.  Many student who join Magoosh make the disastrous pedagogical mistake of binging on questions and ignoring lessons.   Watch lessons!

In the math lessons, the first modules are elementary: if you can pass the quiz on the end of the module, don’t sit through the whole module. At the end of most lessons, there’s a summary screen that outlines what the lesson covered: if you jump ahead to this screen, you will get a good idea about what was covered, and if it’s all elementary to you, you can skip that lesson.  That’s perfectly fine for the first couple modules, but even by the time you get to Integer Properties, there are mathematic ideas not to be underestimated.   It’s a balance: don’t waste time watching lesson after lesson of material you already understand inside-out, but again, lean toward conscientiousness if there’s a chance to understand something more deeply.

The Sentence Correction lessons account for more than 50% of all the Verbal lessons.  The first lessons on Parts of Speech may seem basic, but it’s very important to master the terminology so you understand fully the later discussion.

Group #2: Quant Score 1-6; Verbal Score 7-10
Many of the folks who land in this group are probably verbally-skilled native English speakers.  It’s good that you have such a strong understanding of the verbal concepts.  We need to work on math!  It may be that you were very good at math in other periods of your life and are just a little rusty now.  It may be that you bid a bitter adieu to math sometime in the middle of high school, hoping you would never have to see this dreaded beast again, and now, after an absence of many years, this Grendel has stalked out of the infernal depths to confront you on the GMAT Quant!  Either way, we can help you feel much better about your mathematical prospects on the GMAT.

1) This is the recommended 3-month study plan.  This plan recommends several study resources that you will find helpful.

2) Use the GMAT Math Flashcards = drill these until you know them all

3) For a Magoosh student in this group, probably most of the Verbal lessons would be unnecessary.  It may be good to watch the summary of some lessons, simply to make sure that you are familiar with all the points covered.

4) Of course, watch all the Magoosh math lesson videos.  That plan has you go through the entire sequence, then start at the top, and watch them all again.  If you watch any lesson and are aware you didn’t get all of it, watch it again right away.  Conscientiousness is more important than efficiency in learning!

5) Someone in this group needs to focus on math.  You need to math every single day, especially mental math.  You need to work on developing number sense.  People who love math get excited over all the patterns inherent in numbers: as one explores, one will learn more and more of these patterns.  Of course, someone in this group should watch the eight Magoosh lesson videos in the General Math Strategies module until one remember to practice all these habits every day.

Group #3: Quant Score 7-10; Verbal Score 1-6
A few of the people in this group will be techie American students who have always focused on math & science and who reflexively have avoided “things with words.”  I imagine the majority of folks in this group will be all the very intelligent folks for whom English is not a native language.  If you are in this latter group, then congratulations on learning English well enough to read this blog article!  You have come very far, and we can support you the rest of the way!

1) This is the recommended 3-month study plan.  This plan recommends several study resources that you will find helpful.

2) Use the GMAT Idiom Flashcards = drill these until you know them all

3) If you are this advanced in math, you probably need to see very few math lessons.  Take the quizzes at the end of the Magoosh lessons modules, and if you continue to perform well on these, you are probably in good shape.  If in the course of practice questions, you come across a math concept on which you are not 100% clear, go back to the related lesson to solidify that.  Overall, this is probably not where you need to focus the bulk of your learning.  Doing a lot of math practice would be very important, to keep all your skills sharp and to see the range of variation in GMAT Quant problems.

4) Watching all the Magoosh Verbal lessons is a must.  That study plan has you watch all of them, and then go back to the top and watch them all again.  Some of the other resources in that plan, such as the three MGMAT verbal books, will reinforce the same basic ideas.  On the one hand, everything you need is in the Magoosh lessons, and on the other hand, many people learn many ideas more deeply when they are taught them in two different ways.   It will also be important to watch every video explanation to every Magoosh verbal question, regardless of whether you get the question right or wrong: always be pushing yourself to learn more deeply in every way!

5) As the person weak in math needs to practice mental math daily, the person who needs to boost her verbal performance needs to read daily.   For someone whose native language is something other than English, I would recommend reading difficult sophisticated writings in English for at least an hour a day every single day: that’s a hour over and above any time you spend studying for the GMAT.  Again, a hard habit to implement, but nothing about excellence is easy!

Group #4: Quant Score 7-10; Verbal Score 7-10
If you are in this group, then congratulations!  You already have shown tremendous progress toward an impressive GMAT score.  Now, having said that, I will caution you: getting complacent is the best way to fall short of your potential.  So many people get to this point and then lose a sense of urgency, and this is precisely why so few wind up with scores over 700.  Even though your prospects are good, the worst thing you could do would be to take anything for granted.  You still have to hunger for excellence.  You still have to apply the habits of excellence assiduously.

1) This is the recommended 3-month study plan.  This plan recommends several study resources that you will find helpful.

2) You probably know most of the content of both flashcard decks, but it would be particularly conscientious to run through each just to check.

3) It’s good to do high level reading as part of your preparation.  Certainly, you should read enough to be highly conversant with the major issues in the business world, especially those issue in the sector you would like to enter.   Beyond this, read academic books or journals.  Force yourself to read articles about which you have little expertise or spontaneous interest.

4) It’s always good to practice mental math, and if you have a facility with math, try to challenge yourself in this regard.  For example, in the USA, license plates of privately owned cars tend to have three digit numbers on them: find the prime factorizations of those in your head.  Practice squaring two digit numbers in your head.  Add and subtract fractions in your head.  By the time test day comes, there should be no mental math in which you are not already well practiced.

5) Challenge yourself to push to deeper and deeper levels of understanding.  One of the best ways to do this is to put yourself into a situation in which you have to explain a problem to someone else.  It is one level of understanding to known how to do a problem and be able to do it cold.  It is a higher level if you can walk someone who is confused through the problem step by step, answering all her questions so the problem makes complete sense to her.  You really have to understand something deeply to teach it.   You can do this in a study group, or you can find opportunities on the GMAT forums.

Excellence
Now that we’ve discussed the recommendations for the four cases, I will make a few general comments.  Folks naïvely think getting a good GMAT score is all about finding the best resources with the best content.   Magoosh provides excellent content, and the content supplied by many other companies is also very good.  A large percentage of folks studying for the GMAT have access to excellent content, but only 10% of these test takers cross the magic 700 threshold.  Many many more people have the good content than are able to capitalize on it.   What’s going on?

You see, the focus on the content arises from a fundamental misconception about education.  The misconception is that education is something that the teacher or the GMAT expert does to the student: the teacher is the active giver of education and the student is the passive recipient and consumer.   That is a damaging misapprehension.  In fact, education is something the student does by herself, for herself, to herself, with the support of a teacher or expert.  You are 100% responsible for your own learning, and how much you learn depends considerably more on your own choices that most people appreciate.

Suppose you aspire to a 700+ GMAT score, an excellent score.  One could start in any one of these buckets and achieve that score, but again, your outcome will depend very much on you.  If you want to achieve excellence, then you would be well advised to practice the habits of excellence.  Here, in brief, are some of the more salient habits of excellence.

1) Be assiduous in learning from your mistakes.  This involves the optimistic attitude of always looking for what else you can learn and being grateful for opportunities to refine your understanding.

2) Focus on the process, not on the outcome.  Make your own excellence the standard, not something outside of yourself.

3) Lean toward depth over breadth: understanding ten problems inside-out is much more valuable than having a superficial understanding of 100 problems.

4) Choose conscientiousness over efficiency: if you think you understand something but are not 100% sure, then read the explanation or watch the video again.

5) Insofar as any concept or topic evokes feelings of confusion, anxiety, or dread, make yourself prioritize your engagement with this material.

6) Ask not “is this good enough?” (one of the defining questions of mediocrity); instead, as “what else can I do?”

7) Don’t be quick to check off any concept: instead, push yourself to deeper levels of understanding.

8) Learn the test maker’s priorities and preference in each question type.

9) Practice mindfulness for focus enhancement and stress reduction.

10) Cultivate curiosity as a worldview.

The great philosopher Aristotle (384 – 322 BCE) said, “We are what we repeatedly do.  Excellence, then, is not an act, but a habit.” Your best chance of producing an excellent performance on test day is to practice excellence as a habit, in your GMAT studies and in every area of your life, for the weeks and months leading up to the test.   Develop a passion for bringing the best of yourself to every situation.  Of course, it’s very hard to live that way.  Here, I will remind you of the Great Law of Mediocrity: if you do only what most people consider reasonable to do, then you will wind up with the result that most people get.   If you want to have truly extraordinary results, then everything about your approach from this moment forward should be extraordinary.

 

Good luck in your preparation for the GMAT!  Remember that Magoosh can help you!

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GMAT Official Guide Reading Comprehension #103 [#permalink]

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New post 21 Jun 2016, 11:01
FROM Magoosh Blog: GMAT Official Guide Reading Comprehension #103
We are now taking on the final question in this set—a detail question. Even though the answer to these questions are stated in the passage, they can sometimes be troublesome and tricky. I guarantee you won’t feel tricked at the end of this video.



If you’d like to see how we evaluated the passage, head over to our first video in this series!

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How to Shine in an Overrepresented Applicant Group [#permalink]

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New post 23 Jun 2016, 17:01
FROM Magoosh Blog: How to Shine in an Overrepresented Applicant Group
Business schools often “group” applicants in ethnic, gender, and professional categories for administrative purposes. So if you are a male, Indian IT professional, you will be grouped separately from a female, Norwegian marketing expert. This certainly doesn’t mean that schools are accepting or rejecting applicants based only on these labels and groupings, though, but how you’re initially viewed will impact how the adcom approach your application.

Here are three tips to make you shine, no matter what your applicant category may be and no matter who your direct competition may be:

1. Move beyond the labels.
The admissions process is designed to let the adcoms get to know you as an individual – beyond the labels. Your job is to show the adcoms that you’re not just another face in the crowd of overrepresented applicants, but that you defy categories and labels and are uniquely you. You aren’t Indian, or American, or Indian American or American Indian, not IT and not male – you are YOU.

How to shine: Don’t focus on the group or the label. Spend some time focusing on how you can show your individuality, and emphasize what makes you stand out from the herd. You’ll need to work harder on this than, say, the non-profit female from New Zealand, but it can be done.

2. Use your essay to paint the most colorful picture of you possible.
Write a strong, passionate essay that highlights your personality, varied interests, and talents.

How to shine: Focus on what sets you apart from the group. Use your essay to emphasize your strengths and passions. These are the things that will show that you’re equally as strong a candidate as our friend from New Zealand.

3. Highlight your uniqueness.
When you use your essays and other application components to show what a rare find you are, the adcoms will be able to get a clear picture of you.

How to shine: Stress what makes you stand apart from any group or category you’re placed in. This will help the adcoms see what you – not your group – will be able to contribute to your chosen MBA program or profession.

You’ve seen that you can break away from the crowd and show the adcoms how you shine and will contribute as an individual to their b-school programs. Meanwhile, if you ARE in that large category of Indian candidates, check out our guide, Against the Odds: MBA Admissions for Indian Applicants, for even more tips.

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GMAT Tuesday: Common Flaws in AWA – Errors in Causality [#permalink]

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FROM Magoosh Blog: GMAT Tuesday: Common Flaws in AWA – Errors in Causality
Once you hone your skills for identifying this error, you will see it everywhere. It’s one of the most common flaws that humans make—errors in causality. We are really bad at understanding the relationship of events, actions, and results.



We look at an example prompt, which you can find in the PDF of sample prompts on the mba.com website. Here’s a link to the page where you can download the example prompts.

Be sure to check out this week’s board:
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GMAT Data Sufficiency Logic: Tautological Statements [#permalink]

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FROM Magoosh Blog: GMAT Data Sufficiency Logic: Tautological Statements
First, here are four DS practice problems:

Image

 

Image

2) In the diagram above, line BC touches the circle at point C, and the distance from B to C is 35 cm.  What is the area of the circle?

Statement #1: AB = 25 cm

Statement #2: angle OCB = 90°

 

3) At the 2016 convention for Aim Far Motivational Society (AFMS), each AFMS member had the option of inviting just one non-member guest.  Attending as the single guest of a member is the only way a non-member would be able to attend the convention.  At the 2016 convention, of the AFMS Convention Hall’s seats, 60% were occupied by AFMS members and 10% were occupied by non-member guest.  How many seat does the AFMS Convention Hall have?

Statement #1: If 60% of the members who didn’t bring a guest instead had brought one, then the hall would have been 100% full.

Statement #2:  The number of empty seats was half the number of the AFMS members present.

 

Image

Despite different mathematical subject matters, there’s a common thread running through these four statements.  Solutions will follow this article.

 

Tautologies
The purpose of language is to convey meaning.  For example, the following statements are true statement:

5) Saskatchewan is between Manitoba and Alberta.

6) The Yongle Emperor was the third emperor of the Ming Dynasty.

7) June 28, 1914 was a Sunday.

Each one of these sentences conveys specific information.  They are meaningful statements.  Of course, none of these are facts you need to have memorized for the GMAT.  Theoretically, any one of these could be a relevant sentence in some hypothetical GMAT RC passage.

By contrast, compare these sentences.

8) All pandas are pandas.

9) Every element on the Periodic Table is an element.

10) Each Tuesday in 2003 was between a Monday and a Wednesday.

Each one of these statements doesn’t really tell us anything.  Each one expresses something that is already 100% obvious before the statement was made.  Each statement contains no new information.  These are tautologies.  A tautology is a statement that contains absolutely no new information, because it simply restates what is already known.   In ordinary spoken language, a tautology sounds redundantly obvious: even though it is strictly true, it sounds like nonsense when it is spoken, because we have no idea what the motivation would be of a person speaking such a statement.   None of these could ever be a sentence in a GMAT RC passage, unless the passage were citing one of these as an example of a “tautology.”

 

Mathematical Tautologies
There aren’t too many ways to disguise the same verbal information.  There are many more ways to disguise the same mathematical information. Consider the simple information a + b = c.   This could be rewritten as 2a + b = a + c or as a = b – c.   This last equation, when divided by a, becomes:

Image

This is starting to look very different, but all of these versions contain the same mathematical information.

That was a very simple algebraic example.  In other areas of math, the possibilities for redundant information multiply.   If you are told something is a rectangle, then it is redundant to add that one of the angles is a right angle.   If you are told the average of five numbers is 7, then it is redundant to add that their sum is 35.  If you are told that N is a prime number greater than 20, then it is redundant to add that N is odd.  If you are told that the probability of (P or Q) is less than 1/2, then it is redundant to add that the probability of P alone is less than 1/2.   The examples are endless.  If any redundant statement is added under the pretext of being an additional useful piece of information, such a statement is a tautology, a statement that adds no new useful information.

 

Tautologies in GMAT Data Sufficiency
The basic setup of the GMAT DS is that the prompt provides partial or no information and then asks a question.  The prompt, by itself, is always insufficient.   The general is that each statement is supposed to provide a new piece of mathematical information, and the question is whether each statement, or their combination, provides information sufficient to answer the question.

Suppose one of the two statements is tautological: in other words, rather than add new independent information as statements usually do, it simply restates the information in the prompt or states something directly deducible from the prompt.   Of course, this statement adds nothing to the prompt: since the prompt is already insufficient, the tautological statement would have to be insufficient.  Furthermore, if the other statement, a genuine new piece of information, is also insufficient, combining it with the tautological statement will never produce sufficiency: in other words, one of the statements is tautological, (C) can never be the answer.

Notice that judging that a statement is tautological is a much more powerful logical conclusion that merely judging that the statement is insufficient.  If I decide that Statement #1 is insufficient, then, without looking at Statement #2, I know that the answer could be (B), (C), or (E).  By contrast, if I decide that Statement #1 is tautological, then, without looking at Statement #2, I know that the answer could be only (B) or (E).  If one statement is tautological, the entire DS problem reduces to a single binary choice about the other statement.

There are many different ways to rephrase mathematical information, so it can be tricky to recognize a tautological statement: once you have recognized it, though, the logical implications are powerful.

 

Summary
Each one of the above DS questions has at least one tautological statement.  Do you recognize them?  Among other things, this fact alone guarantees that (C) or (D) cannot be the answer to any of the four.  If you had any insights while reading this blog, give the practice questions above another look.  Here’s another problem of this sort:

11) Half Full Barrel

For 1000+ more practice questions, each with its own video explanation, and a lesson on tautological statements in DS questions, join Magoosh!

 

Practice Problem Explanations
1) Let’s begin by re-arranging the equation in the prompt.

Image

A direct consequence of this prompt equation is the fact that x = 5.  Right away, we see that Statement #2 is not only insufficient but also tautological.  Now we can look at the other statement.

Statement #1: Since we know that x = 5 from the prompt, this becomes 5n+1 = 625.  All we would have to do is divide both side by 5, and we would have the numerical value of xn.  We don’t have to perform this calculation: it’s enough to know that we could.  This statement, alone and by itself, is sufficient.

Answer = (A)

 

2) In the diagram, the line BC is called a tangent line, a line that touches a circle at only one point.  It’s a geometry fact that a tangent line is always perpendicular to the single radius it touches.  Thus, angle OCB must be a right angle.  We know that triangle ACB is a right triangle, with hypotenuse OB.  This is a direct logical consequence of the prompt set-up.  Thus, statement #2 is tautological.  The answer to the DS questions entirely depends on statement #1 alone.

Statement #1: call the radius of the circle x.  Thus, OC = x, CB = 35, and OB = x + 25.  These are the three sides of a right triangle, so:

Image

This gives us an equation for x that we could solve: when we expand the square of the binomial on the right side, we will have an x-squared term on each side, and when these cancel by subtraction, what’s left will be a simple equation for x.  Once we solve this for x, the radius, we could find the area of the circle.  We don’t need to do the calculation: it’s enough to know that we could.  This statement, alone and by itself, is sufficient.

Answer = (A)

 

3) Let the total number of seats be N.  From the prompt, we know 60% of the seats are occupied by members and 10% by non-member guests, 0.6N and 0.1N respectively, 0.7N in total in attendance.  This means that 30% of the seats, 0.3N, are empty.  Right away, we see that the empty seats, 0.3N, are half of the members attending, 0.6N.  Statement #2 is tautological.

Each single non-member must be the guest of a single member.  Thus, if there are 0.1N seats occupied by guests, there must be another 0.1N seats occupied by members who came with a guest.  Therefore, the number of members who did not bring a guest is 0.5N, and 60% of this would be 0.3N.  If each of these 0.3N members invited a guest, there would be an additional 0.3N guests.  If we add these 0.3N guests to all the 0.7N folks already in attendance, we would get N: in other words, we would fill 100% of the seats.  Statement #1 is also tautological.

Both statements are tautological, so no information at all has been added to the prompt, and everything is insufficient.

Answer = (E)

 

4) Start with the proportion.

Image

If we multiply both side by b and divide both sides by c, we get

Image

Multiply both side by two; of course, anything times two is that that plus itself.

Image

Now, subtract b/d from both sides.

Image

This is statement #1, a direct consequence of the prompt statement.  Thus, statement #1 is a tautological statement, which adds nothing to the prompt.  The answer to the DS questions entirely depends on statement #2 alone.

Statement #2: We can take a square-root of both sides.  Normally, we would have to worry about positive/negative signs, but the prompt guarantees that all numbers are positive.

Image

Divide both sides by 5 and by d.  From the prompt, we know that the value of c/d equals the value of a/b.

Image

Statement #2 leads directly to a numerical value for the ratio a/b.  This statement, alone and by itself, is sufficient.

Answer = (B)

 

 

The post GMAT Data Sufficiency Logic: Tautological Statements appeared first on Magoosh GMAT Blog.
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GMAT English [#permalink]

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New post 15 Jul 2016, 10:01
FROM Magoosh Blog: GMAT English
The GMAT, of course, is given in English.  In fact, the GMAT Verbal section assesses a high level of English usage.  This certainly presents a challenge to folks who are learning English as a second language, and it also presents challenges to American students, native speakers, who speak colloquial English and are less familiar with the sophisticated standards of the GMAT.

 

GMAT Verbal Resources for Non-Native Speakers
If English is not your native language, I will assume you now know it well enough to read these blog articles.  How do you get from basic English, TOEFL-level English, to GMAT English?

First of all, if you are still studying for the TOEFL,  I highly recommend Magoosh’s TOEFL product.  If you are interested in both that product and the Magoosh GMAT product, send a note to our student help team asking whether they can give you a deal on the combined product.

Suppose you have done well on the TOEFL and now you want to take the GMAT.  Here are some resources:

1) free GMAT Idiom flashcards

2) an Introduction to the GMAT Verbal section

3) a student perspective on taking the GMAT as a non-native speaker

4) an overview on GMAT Grammar, with links to specific grammar topics

5) the three biggest areas on GMAT Sentence Correction are grammar, logic, and rhetoric.

For students who sign up for Magoosh, we have a large library of Verbal lessons covering every aspect of GMAT Verbal.  Here’s a sample lesson:

Substantive Clauses

You will notice that each lesson has a transcript, so you can read what you hear, and you have the option to play each lesson at a slower speed, in order to integrate what is being said.

Every Magoosh question has its own video explanation.  This kind of immediate feedback on verbal questions is exactly what will accelerate the performance of non-native speakers.  Here’s a sample SC question:

What the eye sees

Here’s a sample CR question:

Violent felonies in Dismaston

Finally, the most effective advice is, as usual, something that requires a lot of effort.  What will most help non-native speakers achieve a high level of proficiency with GMAT Verbal is developing a habit of reading.

 

GMAT English vs. colloquial English
Some folks taking the GMAT have grown up as native English speakers and are very comfortable with colloquial English, but GMAT uses English at a level of sophistication well above the colloquial level.

In fact, the GMAT specifically targets students who are comfortable with colloquial patterns, many of which are not rigorously correct.  Among the areas tested are:

1) less vs. fewer, number vs. amount

2) lie vs. lay

3) due to vs. because of

4) economic vs. economical

5) listing examples: like vs. such as

For folks who grew up in America speaking English, the potential traps are many, precisely because everyday American life is replete with grammar mistakes.  For example, at almost every grocery store in America, you are likely to see the flawed sign “12 items or less.”  If you see nothing wrong with such a sign, the GMAT SC has a trap waiting for you!

While the Magoosh lesson videos on basic grammar might be too easy for you, our lessons that cover such Diction mistakes will benefit you tremendously.

 

Summary
Whether you have learned English as a second language or are looking to improve your colloquial-level English, Magoosh can help you.  In addition to lessons, each Magoosh question has its own video explanation, and this immediate feedback accelerates learning.   Here’s another free practice question:

The income categories

In this modern business world, your written word will often precede you, and on any singular person, you can only make a first impression once—hence the value of communicating in well-spoken English.

 

The post GMAT English appeared first on Magoosh GMAT Blog.
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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GMAT English for TOEFL Students [#permalink]

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New post 21 Jul 2016, 12:01
FROM Magoosh Blog: GMAT English for TOEFL Students
The GMAT, of course, is given in English.  In fact, the GMAT Verbal section assesses a high level of English usage.  This certainly presents a challenge to folks who are learning English as a second language, and it also presents challenges to American students, native speakers, who speak colloquial English and are less familiar with the sophisticated standards of the GMAT.

 

GMAT Verbal Resources for Non-Native Speakers
If English is not your native language, I will assume you now know it well enough to read these blog articles.  How do you get from basic English, TOEFL-level English, to GMAT English?

First of all, if you are still studying for the TOEFL,  I highly recommend Magoosh’s TOEFL product.  If you are interested in both that product and the Magoosh GMAT product, send a note to our student help team asking whether they can give you a deal on the combined product.

Suppose you have done well on the TOEFL and now you want to take the GMAT.  Here are some resources:

1) free GMAT Idiom flashcards

2) an Introduction to the GMAT Verbal section

3) a student perspective on taking the GMAT as a non-native speaker

4) an overview on GMAT Grammar, with links to specific grammar topics

5) the three biggest areas on GMAT Sentence Correction are grammar, logic, and rhetoric.

For students who sign up for Magoosh, we have a large library of Verbal lessons covering every aspect of GMAT Verbal.  Here’s a sample lesson:

Substantive Clauses

You will notice that each lesson has a transcript, so you can read what you hear, and you have the option to play each lesson at a slower speed, in order to integrate what is being said.

Every Magoosh question has its own video explanation.  This kind of immediate feedback on verbal questions is exactly what will accelerate the performance of non-native speakers.  Here’s a sample SC question:

What the eye sees

Here’s a sample CR question:

Violent felonies in Dismaston

Finally, the most effective advice is, as usual, something that requires a lot of effort.  What will most help non-native speakers achieve a high level of proficiency with GMAT Verbal is developing a habit of reading.

 

GMAT English vs. colloquial English
Some folks taking the GMAT have grown up as native English speakers and are very comfortable with colloquial English, but GMAT uses English at a level of sophistication well above the colloquial level.

In fact, the GMAT specifically targets students who are comfortable with colloquial patterns, many of which are not rigorously correct.  Among the areas tested are:

1) less vs. fewer, number vs. amount

2) lie vs. lay

3) due to vs. because of

4) economic vs. economical

5) listing examples: like vs. such as

For folks who grew up in America speaking English, the potential traps are many, precisely because everyday American life is replete with grammar mistakes.  For example, at almost every grocery store in America, you are likely to see the flawed sign “12 items or less.”  If you see nothing wrong with such a sign, the GMAT SC has a trap waiting for you!

While the Magoosh lesson videos on basic grammar might be too easy for you, our lessons that cover such Diction mistakes will benefit you tremendously.

 

Summary
Whether you have learned English as a second language or are looking to improve your colloquial-level English, Magoosh can help you.  In addition to lessons, each Magoosh question has its own video explanation, and this immediate feedback accelerates learning.   Here’s another free practice question:

The income categories

In this modern business world, your written word will often precede you, and on any singular person, you can only make a first impression once—hence the value of communicating in well-spoken English.

 

The post GMAT English for TOEFL Students appeared first on Magoosh GMAT Blog.
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

_________________

Mike McGarry
Magoosh Test Prep

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Official Guide for GMAT Review 2017 Corrections [#permalink]

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New post 22 Jul 2016, 11:01
FROM Magoosh Blog: Official Guide for GMAT Review 2017 Corrections
The below information about The Official Guide for GMAT® Review, 2017 is from the Graduate Management Admission Council – the makers of the GMAT exam. This content was originally posted on The Official GMAT Blog.

Corrections for the Official Guide for GMAT Review 2017
Image

A note from GMAC: We recently released The Official Guide for GMAT® Review, 2017 and we have discovered that this version contains a number of typos that occurred during the publishing process.

We understand that these errors may make it difficult to understand certain content and could affect the study experience for the GMAT exam. Below, we’ve outlined options that provide updated materials. For complete details and a full list of Frequently Asked Questions, please visit: http://wileyactual.com/gmat.

I have the 2017 Official Guide. What should I do?

You have the following options:

1) Use the errata document to replace chapter 4 and make corrections in the other chapters of the Official Guide. (An errata is a list of corrected errors for a book or other published work.)

2) Request a free replacement copy of The Official Guide for GMAT® Review, 2017 which will be shipped when the new, corrected version comes out in mid-September at the latest. For more information, contact your regional Wiley customer support here.

3) For a refund of your The Official Guide for GMAT® Review, 2017, please reference and follow the refund policy for the retailer from which you purchased the Guide.

In addition to this, candidates have access to comparable study materials that enable them to prepare with official GMAT practice questions, such as The Official Guide for GMAT® Verbal Review, 2017 and The Official Guide for GMAT® Quantitative Review, 2017, Free GMATPrep® Software, and more.

Both the Graduate Management Admission Council (GMAC) and Wiley deeply apologize for the inconvenience this may have caused individuals studying for the GMAT exam. We are committed to high-quality publication standards, and moving forward we will make every effort to ensure that our study products are superior.

GMAC customer care representatives are available to answer any questions or concerns at customercare@mba.com.

To inquire about a replacement copy of The Official Guide for GMAT® Review, 2017, contact your regional Wiley customer support here.

 

The post Official Guide for GMAT Review 2017 Corrections appeared first on Magoosh GMAT Blog.
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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GMAT Tuesday: OG Reading Comprehension – Passage #1-4 [#permalink]

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FROM Magoosh Blog: GMAT Tuesday: OG Reading Comprehension – Passage #1-4
Join me, Kevin, for another dive into the Official Guide to the GMAT. This is the first video in a series of 5, which will cover questions #1-4 in the reading comprehension section of the book.



The post GMAT Tuesday: OG Reading Comprehension – Passage #1-4 appeared first on Magoosh GMAT Blog.
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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Does AWA Really Matter for Business School? [#permalink]

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New post 08 Aug 2016, 18:01
FROM Magoosh Blog: Does AWA Really Matter for Business School?
Facts about the Analytical Writing question (AWA) and the GMAT Writing Score
Fact: The current GMAT involves just one writing task, the Analysis of an Argument task, a 30-minute essay you’ll see at the beginning of the test that will give you your GMAT analytical writing score.  The old (pre-2012) GMAT had two essays, but one was cut when Integrated Reasoning was added.

Fact: Like the Integrated Reasoning score, the GMAT Analytic Writing score does not count in your composite GMAT score.  It is a separate score, reported alongside the rest of your GMAT scores.  (Currently, the full GMAT score report includes a Quantitative subscore, a Verbal subscore, and the overall composite GMAT score representing a combination of those two, a separate IR score, and a separate GMAT writing score.  The overall GMAT score is clearly the most important number in the lot.)

Fact: In addition to seeing your overall GMAT score and Q & V subscores, the admissions committee will see your GMAT essay score.

These facts present a question: how much does this GMAT Analytic Writing score matter?  Yes, adcom will see it, but how much does it really matter?


The AWA Task
Before we delve into whether the writing score matters, let’s make sure everyone is on the same page about the task we are discussing.  When you sit down at the computer ready to take your official GMAT, after the few introductory screens, your first real task will be the Analytical Writing Analysis of an Argument task.  The computer will present you with directions and an argument—typically, a massively flawed argument.  You can find the complete list of possible prompt arguments in section 11.6 of the GMAT Official Guide.  This essay can be thought of as a freestyle “Critical Reasoning Weaken the Argument” question: in other words, you will have to produce an essay explaining why this prompt contains a poor argument. Here are some AWA strategies, an example brainstorming session, and an example GMAT essay.

That’s at least an overview of what you need to know about the GMAT writing question: those links will provide more information.  Now, what about the GMAT Writing score?

Image

The GMAT Essay Score: Not so Important?
We certainly could argue that the GMAT Analytical Writing score is not so important.  It’s undeniable that the Quantitative sections and Verbal sections, which contribute to the overall GMAT score, are considerably more important than the separate GMAT writing score.  Arguably, the fact that the AWA section was “cut in half” when IR was added in 2012 is a further indication of relative importance of the GMAT essay and its score.  It’s true that Business school adcom rely on the Quant, Verbal and Composite scores significantly more than the GMAT writing score.  In fact, recent evidence suggest that adcoms also rely on the IR score significantly more than the GMAT essay score.

The GMAT Analytical Writing Score is Less Important, but Not Unimportant
While it’s true that, in your GMAT preparation, Quant and Verbal and even IR deserve more attention than the AWA, it’s also true you can’t completely neglect AWA.  The difference between a 5 or 6 as your GMAT Analytic Writing score will not make or break a business school admission decision, but having an essay score below a 4 could hurt you.

The purpose of the AWA is to see how well you write, how effectively you express yourself in written form.  This is vitally important in the modern business world, where you may conduct extensive deals with folks you only know via email and online chatting.  Some of your important contacts in your business career will know you primarily through your writing, and for some, your writing might be their first experience of you.  You never get a second chance to make a first impression, and when this first impression is in written form, the professional importance of producing high-quality writing is clear.  While you don’t need to write like Melville, you need to be competent.  A GMAT Analytic Writing score below 4 may cause business schools to question your competence.  That’s why it’s important to have at least a decent showing in AWA.

In particular, if English is not your native language, I realize that this makes the AWA essay all the more challenging, but of course a solid performance on the AWA by a non-native speaker would be a powerful testament to how well that student has learned English.  Toward this end, it would be important for any non-native speaker to practice writing the AWA essay and to get high-quality feedback on her essays.

It would be a mistake to devote 30% of your available study time to AWA.  It would also be a mistake to devote 0% to AWA.  Between those, erring on the low side would be appropriate.  If, in a three-month span, you write half a dozen practice essays, and get generally positive feedback on them with respect to the GMAT standards, that should be plenty of preparation.

For concrete advice on improving your GMAT essay score, sign up for Magoosh GMAT.  We have over 200 lesson videos, teaching you all the content and strategy you will need for the GMAT, including a video series specifically addressing the AWA question.  Magoosh is the best way to help not only your GMAT Analytic Writing score, but also every aspect of your GMAT performance.

 

Editor’s Note: This post was originally published in June 2012 and has been updated for freshness, accuracy, and comprehensiveness.

The post Does AWA Really Matter for Business School? appeared first on Magoosh GMAT Blog.
ForumBlogs - GMAT Club’s latest feature blends timely Blog entries with forum discussions. Now GMAT Club Forums incorporate all relevant information from Student, Admissions blogs, Twitter, and other sources in one place. You no longer have to check and follow dozens of blogs, just subscribe to the relevant topics and forums on GMAT club or follow the posters and you will get email notifications when something new is posted. Add your blog to the list! and be featured to over 300,000 unique monthly visitors

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Does AWA Really Matter for Business School?   [#permalink] 08 Aug 2016, 18:01

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