When positive integer n is divided by 3, the remainder is 1.

n = { 4 , 7 , 10 , 13, 16,19 ........}

Bunuel wrote:

When n is divided by 7, the remainder is 5.

n = { 12 ,19 ........}

Bunuel wrote:

What is the smallest positive integer p, such that (n + p) is a multiple of 21?

19 + p = 21{ Smallest multiple of 21 }

So, p = 2

Hence answer is (B) 2

...

]]>

When positive integer n is divided by 3, the remainder is 1.

n = { 4 , 7 , 10 , 13, 16,19 ........}

Bunuel wrote:

When n is divided by 7, the remainder is 5.

n = { 12 ,19 ........}

Bunuel wrote:

What is the smallest positive integer p, such that (n + p) is a multiple of 21?

19 + p = 21{ Smallest multiple of 21 }

So, p = 2

Hence answer is (B) 2

...]]>

Tough and Tricky questions: Coordinate Geometry.

Line L contains the points (2,3) and (p,q). If q = 2, which of the following could be the equation of line m, which is perpendicular to line L?

(A) 2x + y = px + 7

(B) 2x + y = –px

(C) x + 2y = px + 7

(D) y – 7 = x ÷ (p – 2)

(E) 2x + y = 7 – px

Hey Bunuel,

In the above solution instead of y=mx+c how can we get the solution using equation (y-y1)=m(x-x1),if not can you please elaborate why.

...

]]>

Tough and Tricky questions: Coordinate Geometry.

Line L contains the points (2,3) and (p,q). If q = 2, which of the following could be the equation of line m, which is perpendicular to line L?

(A) 2x + y = px + 7

(B) 2x + y = –px

(C) x + 2y = px + 7

(D) y – 7 = x ÷ (p – 2)

(E) 2x + y = 7 – px

Hey Bunuel,

In the above solution instead of y=mx+c how can we get the solution using equation (y-y1)=m(x-x1),if not can you please elaborate why.

...]]>

If x < y < z and y-x > 5, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?

Fromwhere x is an even integer &least possible value of z - x?

we can have x < y as 2 < 7 , where y - x = 5

From x < y < z andy and z are odd integers

We have x < y < z = 2 < 7 < 9

So,least possible value of z - x? = 9 - 2 => 7

...

]]>

If x < y < z and y-x > 5, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?

Fromwhere x is an even integer &least possible value of z - x?

we can have x < y as 2 < 7 , where y - x = 5

From x < y < z andy and z are odd integers

We have x < y < z = 2 < 7 < 9

So,least possible value of z - x? = 9 - 2 => 7

...]]>

The similarity between the two below expressions always causes me doubt. To confirm, is there a fundamental difference between ...

1) sq. root ([(x^2)] ) - two possible solutions (positive and negative, driven by the even exponent)

2)[(sq. root x)] ^2 - one possible solution; even root yields one (positive) solution

hi! mystseen, this is my explanation...

sq. root(A) is a kind of equation.

...

]]>

The similarity between the two below expressions always causes me doubt. To confirm, is there a fundamental difference between ...

1) sq. root ([(x^2)] ) - two possible solutions (positive and negative, driven by the even exponent)

2)[(sq. root x)] ^2 - one possible solution; even root yields one (positive) solution

hi! mystseen, this is my explanation...

sq. root(A) is a kind of equation.

...]]>

A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average(arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?

(A) 1/20

(B) 1/6

(C) 1/5

(D) 4/21

(E) 5/21

Given : 21 numbers in a list including n. n = 4 times the average of other 20 numbers.

Assume the average to be x

n = 4x - (i)

Average = Sum/20

Sum of other 20 numbers = 20x - (ii)

n/Sum of other 21 numbers =\( \frac{4x}{(4x + 20x)} =\)

...

]]>

A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average(arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?

(A) 1/20

(B) 1/6

(C) 1/5

(D) 4/21

(E) 5/21

Given : 21 numbers in a list including n. n = 4 times the average of other 20 numbers.

Assume the average to be x

n = 4x - (i)

Average = Sum/20

Sum of other 20 numbers = 20x - (ii)

n/Sum of other 21 numbers =\( \frac{4x}{(4x + 20x)} =\)

...]]>

This is an example of a 'limit' question (wherein the question asks for a minimum or maximum value based on a series of restrictions).

Here, we're told that 15 people must each contribute AT LEAST $1 to a total of $20. We're asked for the MAXIMUM that could be contributed by any one person.

To start, we need to minimize 14 people so that the 15th person can be 'maximized.' The minimal amount for each person is $1, so those 14 people would have to contribute 14($1) = $14 at the minimum.

...

]]>

This is an example of a 'limit' question (wherein the question asks for a minimum or maximum value based on a series of restrictions).

Here, we're told that 15 people must each contribute AT LEAST $1 to a total of $20. We're asked for the MAXIMUM that could be contributed by any one person.

To start, we need to minimize 14 people so that the 15th person can be 'maximized.' The minimal amount for each person is $1, so those 14 people would have to contribute 14($1) = $14 at the minimum.

...]]>

Extension : abcd

Since all 4 nos. need to be in the extension, numbers cannot be repeated

d( can be either 2 or 6..) so 2 ways

c: 3 ways

b: 2 ways

a: 1 way

=2*2*3

=12

]]>

Extension : abcd

Since all 4 nos. need to be in the extension, numbers cannot be repeated

d( can be either 2 or 6..) so 2 ways

c: 3 ways

b: 2 ways

a: 1 way

=2*2*3

=12]]>

This question can be solved using the Work Formula:

Work = (A)(B)/(A+B) where A and B are the individual completion rates of the respective entities (for the same job).

We're told that one machine takes 10 minutes to complete a job and another machine takes 12 minutes to complete the same job. Plugging in those values gets us...

(10)(12)/(10+12) = 120/22 = 5 10/22 = 5 5/11 minutes

Final Answer:

[Reveal] Spoiler:

C

GMAT assassins aren't born, they're made,

Rich

]]>

This question can be solved using the Work Formula:

Work = (A)(B)/(A+B) where A and B are the individual completion rates of the respective entities (for the same job).

We're told that one machine takes 10 minutes to complete a job and another machine takes 12 minutes to complete the same job. Plugging in those values gets us...

(10)(12)/(10+12) = 120/22 = 5 10/22 = 5 5/11 minutes

Final Answer:

[Reveal] Spoiler:

C

GMAT assassins aren't born, they're made,

Rich]]>

This question can be solved by TESTing THE ANSWERS. From the prompt, we know that the three people have taught for a total of 96 years and that Virginia has taught for 9 more years than Adrienne and for 9 fewer years than Dennis. So Dennis taught the HIGHEST number of years (meaning that he had to have taught MORE than 96/3 = 32 years). Looking at the Answers, let's start with D....

Answer D: 41 years

IF....

Dennis = 41 years taught

Virginia = 41 - 9 = 32 years taught

Adrienne = 32 -

...

]]>

This question can be solved by TESTing THE ANSWERS. From the prompt, we know that the three people have taught for a total of 96 years and that Virginia has taught for 9 more years than Adrienne and for 9 fewer years than Dennis. So Dennis taught the HIGHEST number of years (meaning that he had to have taught MORE than 96/3 = 32 years). Looking at the Answers, let's start with D....

Answer D: 41 years

IF....

Dennis = 41 years taught

Virginia = 41 - 9 = 32 years taught

Adrienne = 32 -

...]]>

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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Myra drove at an average speed of 30 miles per hour for some time and then at an average speed of 60 miles/hr for the rest of the journey. If she made no stops during the trip and her average speed for the entire journey was 50 miles per hour, for what fraction of the total time did she drive at 30 miles/hour?

(A) 1/5

(B) 1/3

(C) 2/5

(D) 2/3

(E) 3/5

Kudos for a correct solution.

We don't need to get into calculations for solving this questions. We can use the concept of weighted averages.

One

...

]]>

Myra drove at an average speed of 30 miles per hour for some time and then at an average speed of 60 miles/hr for the rest of the journey. If she made no stops during the trip and her average speed for the entire journey was 50 miles per hour, for what fraction of the total time did she drive at 30 miles/hour?

(A) 1/5

(B) 1/3

(C) 2/5

(D) 2/3

(E) 3/5

Kudos for a correct solution.

We don't need to get into calculations for solving this questions. We can use the concept of weighted averages.

One

...]]>

QUANT 4-PACK SERIES Data Sufficiency Pack 4 Question 2 Z is a positive integer...

Z is a positive integer greater than 3. How many distinct prime factors does (Z + 1)(Z – 1) have?

1)Z is not even

2)Z is not a multiple of 5

Hi All,

This question can be solved by TESTing VALUES. We're told that Z is a POSITIVE INTEGER greater than 3. We're asked for the number of DISTINCT (meaning 'different') prime factors in (Z + 1)(Z – 1).

To start, we can rewrite (Z + 1)(Z – 1) as\(Z^{2}\) - 1

1)

...

]]>

QUANT 4-PACK SERIES Data Sufficiency Pack 4 Question 2 Z is a positive integer...

Z is a positive integer greater than 3. How many distinct prime factors does (Z + 1)(Z – 1) have?

1)Z is not even

2)Z is not a multiple of 5

Hi All,

This question can be solved by TESTing VALUES. We're told that Z is a POSITIVE INTEGER greater than 3. We're asked for the number of DISTINCT (meaning 'different') prime factors in (Z + 1)(Z – 1).

To start, we can rewrite (Z + 1)(Z – 1) as\(Z^{2}\) - 1

1)

...]]>

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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]]>

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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QUANT 4-PACK SERIES Data Sufficiency Pack 4 Question 3 On a number line...

On a number line, the distance from point A to zero is greater than the distance from point B to zero. Does point C lie between points A and B on the number line?

1)ABC > 0

2)|A| > |B| > |C|

Hi All,

From the first sentence, we're told that A is FARTHER from 0 on a number line than B is from 0. This essentially means that |A| > |B|. It's possible that these 2 variables are both positive, both negative or

...

]]>

QUANT 4-PACK SERIES Data Sufficiency Pack 4 Question 3 On a number line...

On a number line, the distance from point A to zero is greater than the distance from point B to zero. Does point C lie between points A and B on the number line?

1)ABC > 0

2)|A| > |B| > |C|

Hi All,

From the first sentence, we're told that A is FARTHER from 0 on a number line than B is from 0. This essentially means that |A| > |B|. It's possible that these 2 variables are both positive, both negative or

...]]>

QUANT 4-PACK SERIES Data Sufficiency Pack 4 Question 4 3 siblings - Alan, Betty and Carl...

3 siblings - Alan, Betty and Carl - were the only ones to receive part of a $300,000 inheritance. Did any of the three receive more than forty percent of the total inheritance?

1) Carl received a larger inheritance than Alan and a larger inheritance than Betty.

2) The combined total of Alan’s and Betty’s inheritances was equal to three times Betty’s inheritance.

...

]]>

QUANT 4-PACK SERIES Data Sufficiency Pack 4 Question 4 3 siblings - Alan, Betty and Carl...

3 siblings - Alan, Betty and Carl - were the only ones to receive part of a $300,000 inheritance. Did any of the three receive more than forty percent of the total inheritance?

1) Carl received a larger inheritance than Alan and a larger inheritance than Betty.

2) The combined total of Alan’s and Betty’s inheritances was equal to three times Betty’s inheritance.

...]]>

A. 1/8

B. 1/4

C. 1/2

D. 3/4

E. 7/8

Alt Explanation-

When the fair dice and fair coin numbered 1 and 2 are rolled ,the sum is equally likely to be even or odd.Hence probability is 50%,i.e 1/2.

]]>

A. 1/8

B. 1/4

C. 1/2

D. 3/4

E. 7/8

Alt Explanation-

When the fair dice and fair coin numbered 1 and 2 are rolled ,the sum is equally likely to be even or odd.Hence probability is 50%,i.e 1/2.]]>

say angle CAB=y

since sum of angles in a triangle is 180

x+y+45=180

x+y=135 equation 1

line AD is dividing BC in 2:1 ratio

hence

X+2/3Y+60=180

X+2/3y=120 equation 2

solving equation 1 &2 we get x=75

answer is D

x+y = 135---1

x+2/3y = 120----2

subtracting 2 from 1

1/3 y = 15

y =45.

Substituting y =45 in eq 1

x+45 = 135

x = 90.

Whats my mistake

]]>

say angle CAB=y

since sum of angles in a triangle is 180

x+y+45=180

x+y=135 equation 1

line AD is dividing BC in 2:1 ratio

hence

X+2/3Y+60=180

X+2/3y=120 equation 2

solving equation 1 &2 we get x=75

answer is D

x+y = 135---1

x+2/3y = 120----2

subtracting 2 from 1

1/3 y = 15

y =45.

Substituting y =45 in eq 1

x+45 = 135

x = 90.

Whats my mistake]]>

All the fractions can be written as 1 - 3/(Some number)

The largest denominator would make the number highest

]]>

All the fractions can be written as 1 - 3/(Some number)

The largest denominator would make the number highest]]>

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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]]>

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Official Solution:

Last year, seniors at Jasper County’s public high schools performed worse on standardized college-entrance exams than their peers at Nesbit County’s public high schools. In recent years, more and more Jasper County residents have been enrolling their children in private high schools, where the teacher-to-student ratio is traditionally lower than in public schools, and enrollment in Jasper County’s public high schools has dwindled as a result. Based only on the information above, parents residing in Jasper County and concerned about their child’s academic future should pursue which of the following courses of action?

...

]]>

Official Solution:

Last year, seniors at Jasper County’s public high schools performed worse on standardized college-entrance exams than their peers at Nesbit County’s public high schools. In recent years, more and more Jasper County residents have been enrolling their children in private high schools, where the teacher-to-student ratio is traditionally lower than in public schools, and enrollment in Jasper County’s public high schools has dwindled as a result. Based only on the information above, parents residing in Jasper County and concerned about their child’s academic future should pursue which of the following courses of action?

...]]>

My take on this.

If the non-auditing and audit sections are broken up then there might be a chance that audit and non-audit section can get combined then again they could have instead of Four big firms, 10 small firms(with both audit and non-audit) but Corporates can't separate them out.

However, in this question POE is much better because other options are notrelevant.

p2bhokie wrote:

Although I marked the answer correctly, can someone please explain in greater detail

ht option...I selected...

]]>

My take on this.

If the non-auditing and audit sections are broken up then there might be a chance that audit and non-audit section can get combined then again they could have instead of Four big firms, 10 small firms(with both audit and non-audit) but Corporates can't separate them out.

However, in this question POE is much better because other options are notrelevant.

p2bhokie wrote:

Although I marked the answer correctly, can someone please explain in greater detail

ht option...I selected...]]>

If you're planning to apply soon, then you'll have to put some serious work into your applications WHILE you continue to study for the GMAT.

1) Have you taken the actual GMAT yet? If so, then how did you score? If not, then how have you scored on your practice CATs?

GMAT assassins aren't born, they're made,

Rich

]]>

If you're planning to apply soon, then you'll have to put some serious work into your applications WHILE you continue to study for the GMAT.

1) Have you taken the actual GMAT yet? If so, then how did you score? If not, then how have you scored on your practice CATs?

GMAT assassins aren't born, they're made,

Rich]]>

Raymond took several days to mow a certain lawn. He mowed 1/3 of the lawn the first day

Let the total work be 12

Work completed after\(1^{st}\) day is 4 , work left is8

Bunuel wrote:

1/2 of the remaining unmowed portion the second day

Work completed after\(2^{nd}\) day is 4 , work left is 4

Bunuel wrote:

3/4 of the remaining unmowed portion the third day

Work completed after\(3^{rd}\) day is 3 , work left is 1

Bunuel wrote:

What fraction of the lawn remained unmowed at the end of the third day?

Part of work remaining = Part of work left

...

]]>

Raymond took several days to mow a certain lawn. He mowed 1/3 of the lawn the first day

Let the total work be 12

Work completed after\(1^{st}\) day is 4 , work left is8

Bunuel wrote:

1/2 of the remaining unmowed portion the second day

Work completed after\(2^{nd}\) day is 4 , work left is 4

Bunuel wrote:

3/4 of the remaining unmowed portion the third day

Work completed after\(3^{rd}\) day is 3 , work left is 1

Bunuel wrote:

What fraction of the lawn remained unmowed at the end of the third day?

Part of work remaining = Part of work left

...]]>

An association of mathematics teachers has 1,260 members. Only 525 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast?

(A) 75%

(B) 58%

(C) 42%

(D) 34%

(E) 25%

No of voters who cast votes in the election is 3/5 of 525 = 315

% of voters who voted for the winning candidate is (315/1260 )100 = 25%

Hence answer is 25%

Note : 60%

...

]]>

An association of mathematics teachers has 1,260 members. Only 525 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast?

(A) 75%

(B) 58%

(C) 42%

(D) 34%

(E) 25%

No of voters who cast votes in the election is 3/5 of 525 = 315

% of voters who voted for the winning candidate is (315/1260 )100 = 25%

Hence answer is 25%

Note : 60%

...]]>

A square picture frame has an outer perimeter of 36 inches and is 1 inch wide on all sides. What is the inner perimeter of the frame, in inches?

(A) 27

(B) 27.5

(C) 28

(D) 31.5

(E) 32

From the figure below , sides of the inner sqaure is 7 inch

So, perimeter of the Inner square is 7*4 = 28 inches...

Answer is (C)

Attachments

Square.jpg [ 15.6 KiB | Viewed 48 times ]

]]>

A square picture frame has an outer perimeter of 36 inches and is 1 inch wide on all sides. What is the inner perimeter of the frame, in inches?

(A) 27

(B) 27.5

(C) 28

(D) 31.5

(E) 32

From the figure below , sides of the inner sqaure is 7 inch

So, perimeter of the Inner square is 7*4 = 28 inches...

Answer is (C)

Attachments

Square.jpg [ 15.6 KiB | Viewed 48 times ]

]]>

If n is a positive integer and if (n^3 - n)/(n+1) = 240, then what is the value of n?

A. 12

B. 16

C. 17

D. 20

E. 48

\(\frac{(n^3 - n)}{(n+1)}\) =240

\(\frac{(n^3 - n)}{(n+1)}\) =\((16 )(15)\)

\(\frac{n(n^2 - 1)}{(n+1)}\) = \((16 )(15)\)

\(\frac{n(n - 1)(n+1)}{(n+1)}\) \((16 )(15)\)

\(n(n - 1)\) = \((16 )(15)\)

So,\(n\) =\(16\)

Hence answer is definitely (B)

...

]]>

If n is a positive integer and if (n^3 - n)/(n+1) = 240, then what is the value of n?

A. 12

B. 16

C. 17

D. 20

E. 48

\(\frac{(n^3 - n)}{(n+1)}\) =240

\(\frac{(n^3 - n)}{(n+1)}\) =\((16 )(15)\)

\(\frac{n(n^2 - 1)}{(n+1)}\) = \((16 )(15)\)

\(\frac{n(n - 1)(n+1)}{(n+1)}\) \((16 )(15)\)

\(n(n - 1)\) = \((16 )(15)\)

So,\(n\) =\(16\)

Hence answer is definitely (B)

...]]>

Suppose x & y are two integers such that x + y = 6

(A) both integers are even -Wrong

Can we have x + y = 6 when both are not even? Yes. (1+5=6)

(B) both integers are odd -Wrong

Can we have x + y = 6 when both are not odd? Yes. (2+4=6)

(C) both integers are positive -Wrong

Can we have x + y = 6 when only one is positive? Yes (7 + (-1) = 6)

(D) if one integer

...

]]>

Suppose x & y are two integers such that x + y = 6

(A) both integers are even -Wrong

Can we have x + y = 6 when both are not even? Yes. (1+5=6)

(B) both integers are odd -Wrong

Can we have x + y = 6 when both are not odd? Yes. (2+4=6)

(C) both integers are positive -Wrong

Can we have x + y = 6 when only one is positive? Yes (7 + (-1) = 6)

(D) if one integer

...]]>

Diana bought a stereo for $530, which was the retail price plus a 6 percent sales tax.

Let the retail price of the stereo be 100

Diana bought the stereo at106

Bunuel wrote:

in a neighboring state where she would have paid a sales tax of 5 percent?

Price of the stereo in neighboring state is 105

Bunuel wrote:

How much money could she have saved if she had bought the stereo at the same retail price in a neighboring state

Savings possible by buying the stereo from the neighboring state is 106 - 105 = 1

Bunuel wrote:

Diana bought a stereo

...

]]>

Diana bought a stereo for $530, which was the retail price plus a 6 percent sales tax.

Let the retail price of the stereo be 100

Diana bought the stereo at106

Bunuel wrote:

in a neighboring state where she would have paid a sales tax of 5 percent?

Price of the stereo in neighboring state is 105

Bunuel wrote:

How much money could she have saved if she had bought the stereo at the same retail price in a neighboring state

Savings possible by buying the stereo from the neighboring state is 106 - 105 = 1

Bunuel wrote:

Diana bought a stereo

...]]>

In 1985 a company sold a brand of shoes to retailers for a fixed price per pair. In 1986 the number of pairs of the shoes that the company sold to retailers decreased by 20 percent, while the price per pair increased by 20 percent. If the company’s revenue from the sale of the shoes in 1986 was $3.0 million, what was the approximate revenue from the sale of the shoes in 1985 ?

(A) $2.4 million

(B) $2.9 million

(C) $3.0 million

(D) $3.1 million

(E) $3.6 million

A am using a

...

Attachments

Revenue.PNG [ 2.61 KiB | Viewed 60 times ]

]]>

In 1985 a company sold a brand of shoes to retailers for a fixed price per pair. In 1986 the number of pairs of the shoes that the company sold to retailers decreased by 20 percent, while the price per pair increased by 20 percent. If the company’s revenue from the sale of the shoes in 1986 was $3.0 million, what was the approximate revenue from the sale of the shoes in 1985 ?

(A) $2.4 million

(B) $2.9 million

(C) $3.0 million

(D) $3.1 million

(E) $3.6 million

A am using a

...

Attachments

Revenue.PNG [ 2.61 KiB | Viewed 60 times ]

]]>

x= y + 10

Answer D

]]>

x= y + 10

Answer D]]>

Which of the following fractions, if written as a decimal, would have a 2 in the thousandths place ?

(A) 3/11

(B) 7/9

(C) 1/8

(D) 4/7

(E) 1/6

(A) 3/11 = 0.2727272727....

Answer: A

Cheers,

Brent

]]>

Which of the following fractions, if written as a decimal, would have a 2 in the thousandths place ?

(A) 3/11

(B) 7/9

(C) 1/8

(D) 4/7

(E) 1/6

(A) 3/11 = 0.2727272727....

Answer: A

Cheers,

Brent]]>

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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]]>

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.]]>

If m/7 is an integer, then each of the following must be an integer EXCEPT

A. (m - 28)/7

B. (m + 21)/7

C. 14m/98

D. (m^2 - 49)/49

E. (m + 14)/14

The question says "each of the followingmust be an integer EXCEPT"

So, if we can find an instance where an answer choice is NOT an integer, then that will be the correct answer.

Given: m/7 is an integer

So, m could equal7

Now plug m =7 into the answer choices:

A. (7 - 28)/7 = -3. This is an integer

B. (7 + 21)/7 = 4. This is an integer

C.

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If m/7 is an integer, then each of the following must be an integer EXCEPT

A. (m - 28)/7

B. (m + 21)/7

C. 14m/98

D. (m^2 - 49)/49

E. (m + 14)/14

The question says "each of the followingmust be an integer EXCEPT"

So, if we can find an instance where an answer choice is NOT an integer, then that will be the correct answer.

Given: m/7 is an integer

So, m could equal7

Now plug m =7 into the answer choices:

A. (7 - 28)/7 = -3. This is an integer

B. (7 + 21)/7 = 4. This is an integer

C.

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Number of votes cast against the proposal = A

F = A + 80 -- 1

Since , the number of votes against the proposal was 40 percent of the total vote

A= (40/100)*T = .4T -- 2

=> F = (60/100)*T = .6T -- 3

From equations 1 , 2 and 3 ,we get

.2T = 80

=> T= 400

Answer B

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Number of votes cast against the proposal = A

F = A + 80 -- 1

Since , the number of votes against the proposal was 40 percent of the total vote

A= (40/100)*T = .4T -- 2

=> F = (60/100)*T = .6T -- 3

From equations 1 , 2 and 3 ,we get

.2T = 80

=> T= 400

Answer B]]>

abhi47 wrote:

A gambler rolls three fair six-sided dice. What is the probability that two of the dice show the same number, but the third shows a different number?

Responding to apm.

Combinations approach:

Total # of outcomes is\(6^3\) ;

Favorable outcomes are all possible scenarios of XXY:

\(C^1_6*C^1_5*\frac{3!}{2!}=6*5*3=90\) where\(C^1_6\) is # of ways to pick X (the number which shows twice),\(C^1_5\) is # of ways to pick Y (out of 5 numbers left) and\(\frac{3!}{2!}\) is # of permutation of 3 letters XXY out of which

...

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abhi47 wrote:

A gambler rolls three fair six-sided dice. What is the probability that two of the dice show the same number, but the third shows a different number?

Responding to apm.

Combinations approach:

Total # of outcomes is\(6^3\) ;

Favorable outcomes are all possible scenarios of XXY:

\(C^1_6*C^1_5*\frac{3!}{2!}=6*5*3=90\) where\(C^1_6\) is # of ways to pick X (the number which shows twice),\(C^1_5\) is # of ways to pick Y (out of 5 numbers left) and\(\frac{3!}{2!}\) is # of permutation of 3 letters XXY out of which

...]]>

I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Mod(x) is always + or zero, here x is not 0, hence +ve.

how can x>-1 be the right answer. Take x=0.5, then the soln gives 1<0.5. -not true. Please elaborate

Please check the discussion of this question here: if-x-0-and-x-x-x-which-of-the-following-must-be-true-143572.htmlif-x-0-and-x-x-x-which-of-the-following-must-be-true-143572.html