Statement 1: true, because 40 is a multiple of 20

Statement 2: true, because 40 + 6 = 46, which is a multiple of3

However n is not a multiple of 15.

If n=60

Statement 1: true, because 60 is a multiple of 20

Statement 2: true, because 60 + 6 = 66, which is a multiple of3

In this case n is a multiple of 15.

So, I fail to understand why answer C is correct, when from the example above we can observe that the statements put together can yield different results for N which are and are

...

]]>

Statement 1: true, because 40 is a multiple of 20

Statement 2: true, because 40 + 6 = 46, which is a multiple of3

However n is not a multiple of 15.

If n=60

Statement 1: true, because 60 is a multiple of 20

Statement 2: true, because 60 + 6 = 66, which is a multiple of3

In this case n is a multiple of 15.

So, I fail to understand why answer C is correct, when from the example above we can observe that the statements put together can yield different results for N which are and are

...]]>

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.

]]>

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.]]>

x^2-4x-60=0

x = 10 or -6

So 2x+3 gives 23 or -9

A

Sent from my iPhone using GMAT Club Forum mobile app

]]>

x^2-4x-60=0

x = 10 or -6

So 2x+3 gives 23 or -9

A

Sent from my iPhone using GMAT Club Forum mobile app]]>

A)zero

B)one

C)two

D)four

E)six

]]>

A)zero

B)one

C)two

D)four

E)six]]>

12kgs of alloy1 has P1% of iron in it. 6 kgs of alloy2 has P2% iron in it ( P1 not equal to P2). X kgs of each alloy is cut and then fused with the remaining part of the other alloy. If two resulting alloys have equal percentage of iron, find X?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

Consider Kudos if you like the question.

Let P1 be a and P2 be b for simplicity.....

{(12-x)*a+x*b}/12={(6-x)*P2+x*P1}/6......

(12a-xa+xb)/12=(6b-xb+xa)/6....

72a-6xa+6xb=72b-12xb+12xa

72(a-b)=18x(a-b).....

72=18x.....x=72/18=4..

D

...

]]>

12kgs of alloy1 has P1% of iron in it. 6 kgs of alloy2 has P2% iron in it ( P1 not equal to P2). X kgs of each alloy is cut and then fused with the remaining part of the other alloy. If two resulting alloys have equal percentage of iron, find X?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

Consider Kudos if you like the question.

Let P1 be a and P2 be b for simplicity.....

{(12-x)*a+x*b}/12={(6-x)*P2+x*P1}/6......

(12a-xa+xb)/12=(6b-xb+xa)/6....

72a-6xa+6xb=72b-12xb+12xa

72(a-b)=18x(a-b).....

72=18x.....x=72/18=4..

D

...]]>

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.

]]>

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.]]>

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.

]]>

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.]]>

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.

]]>

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.]]>

Lets say the complete job is equal to 1 out of which Elena did\(\frac{11}{18}\) of the job.

So, we know that Andy did1-\(\frac{11}{18}\) of the job =\(\frac{7}{18}\)

We are given that the difference between their earning is $154 which is going to be difference in work into hourly pay.

Difference in work =\(\frac{11}{18}\) -\(\frac{7}{18}\) =\(\frac{4}{18}\)

HTH

...

]]>

Lets say the complete job is equal to 1 out of which Elena did\(\frac{11}{18}\) of the job.

So, we know that Andy did1-\(\frac{11}{18}\) of the job =\(\frac{7}{18}\)

We are given that the difference between their earning is $154 which is going to be difference in work into hourly pay.

Difference in work =\(\frac{11}{18}\) -\(\frac{7}{18}\) =\(\frac{4}{18}\)

HTH

...]]>

Bunuel

In GMAT will there be something by which we can differentiate that the question is asking

m = 115*n or a 4-digit no m = 115n (where the units digit is n)

If it were 4-digit number 115n, where n is an units digit then it would be explicitly mentioned. Otherwise, 115n always means 115*n.

]]>

Bunuel

In GMAT will there be something by which we can differentiate that the question is asking

m = 115*n or a 4-digit no m = 115n (where the units digit is n)

If it were 4-digit number 115n, where n is an units digit then it would be explicitly mentioned. Otherwise, 115n always means 115*n.]]>

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.

]]>

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.]]>

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.

]]>

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.]]>

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.

]]>

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.]]>

might be a little bit off topic.

But do I have to understand (be able to solve) these very hard questions if I am aiming for a low 600?

]]>

might be a little bit off topic.

But do I have to understand (be able to solve) these very hard questions if I am aiming for a low 600?]]>

Bunuel wrote:

duahsolo wrote:

How many integer points lie between points A and B on the line segment AB, if A is (5, 7) and B is (10, -3)?

A) 4

B) 5

C) 6

D) 10

E) 15

A) 4

B) 5

C) 6

D) 10

E) 15

Merging topics. Please refer to the discussionabove.

Similar questions to practice:

in-the-figure-above-how-many-of-the-points-on-line-segment-108673.html

...

]]>

Bunuel wrote:

duahsolo wrote:

How many integer points lie between points A and B on the line segment AB, if A is (5, 7) and B is (10, -3)?

A) 4

B) 5

C) 6

D) 10

E) 15

A) 4

B) 5

C) 6

D) 10

E) 15

Merging topics. Please refer to the discussionabove.

Similar questions to practice:

in-the-figure-above-how-many-of-the-points-on-line-segment-108673.html

...]]>

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.

]]>

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.]]>

In order to determine whether r/s is a terminating decimal, we need to know what is at the denominator.

Statement B clearly states that denominator can never be 3 or 7. Hence, Statement B is sufficient. Answer B.

]]>

If r and s are positive integers is r/s a terminating decimal?

1) r is a factor of 100

2) s is a factor of 200

* A solution will be posted in two days.

In order to determine whether r/s is a terminating decimal, we need to know what is at the denominator.

Statement B clearly states that denominator can never be 3 or 7. Hence, Statement B is sufficient. Answer B.]]>

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.

]]>

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.]]>

]]>

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.

]]>

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.]]>

The distance between the unknown vertices to the midpoint is half the diagonal:

(x−3)2+(y−4)2=(52√2)2=13(x−3)2+(y−4)2=(522)2=13;

I don't understand what this step is doing?

This step is finding the distance from vertex A(x,y) to mid point M(3,4) or the length of AM you can say.

since AC is also a diagonal, AM will be half its length (whichis\sqrt{52} and diagonals of a square are equal in length.)

I hope it clears your doubt.

...

]]>

The distance between the unknown vertices to the midpoint is half the diagonal:

(x−3)2+(y−4)2=(52√2)2=13(x−3)2+(y−4)2=(522)2=13;

I don't understand what this step is doing?

This step is finding the distance from vertex A(x,y) to mid point M(3,4) or the length of AM you can say.

since AC is also a diagonal, AM will be half its length (whichis\sqrt{52} and diagonals of a square are equal in length.)

I hope it clears your doubt.

...]]>

A---------6---------C-------4--------B

here

AC + BC = 10

and

AB + AC > 10

So we cannot say for sure that AB is less than 10.

...

]]>

A---------6---------C-------4--------B

here

AC + BC = 10

and

AB + AC > 10

So we cannot say for sure that AB is less than 10.

...]]>

Bunuel wrote:

nglekel wrote:

Bunuel,

What if line p has a negative y intercept but line n has a positive intercept? Wouldn't that give the oposite answer?

What if line p has a negative y intercept but line n has a positive intercept? Wouldn't that give the oposite answer?

If line p has a negative y-intercept then its slope is positive and it will still be more than the slope of n, with positive y-intercept (if the slope of n will be positive than p will still be steeper than n, and if the slope of n is negative it obviously will be less than positive slope of p). Consider first image and rotate line n (blue) so that it to have positive

...

]]>

Bunuel wrote:

nglekel wrote:

Bunuel,

What if line p has a negative y intercept but line n has a positive intercept? Wouldn't that give the oposite answer?

What if line p has a negative y intercept but line n has a positive intercept? Wouldn't that give the oposite answer?

If line p has a negative y-intercept then its slope is positive and it will still be more than the slope of n, with positive y-intercept (if the slope of n will be positive than p will still be steeper than n, and if the slope of n is negative it obviously will be less than positive slope of p). Consider first image and rotate line n (blue) so that it to have positive

...]]>

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.

]]>

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.]]>

I think this is a high-quality question and I don't agree with the explanation. i Think these eqation can be solved

Let salary be 4x and 3x

Let Saving be 3y and 2y

Expenditure = 4x-3y +3x-2y=7x-5y

20,000=7x-5y

therefore only Values of X and Y which satisfies these equation are X=5000 and Y=3000

20,000=7x-5y has infinitely many solutions. You cannot solve two variable linear equation to get only one solution (assuming you don't have any other constraints).

...

]]>

I think this is a high-quality question and I don't agree with the explanation. i Think these eqation can be solved

Let salary be 4x and 3x

Let Saving be 3y and 2y

Expenditure = 4x-3y +3x-2y=7x-5y

20,000=7x-5y

therefore only Values of X and Y which satisfies these equation are X=5000 and Y=3000

20,000=7x-5y has infinitely many solutions. You cannot solve two variable linear equation to get only one solution (assuming you don't have any other constraints).

...]]>

Why is 1 and 2 together not sufficient?

If I used a= -4 and b = -3, making statement 1 to 16 = 9+7, which will give the answer to a - b = -4-(-3) = -1.

The correct answer to the question is A, which means that the first statement alone is sufficient while second statement alone is not.

]]>

Why is 1 and 2 together not sufficient?

If I used a= -4 and b = -3, making statement 1 to 16 = 9+7, which will give the answer to a - b = -4-(-3) = -1.

The correct answer to the question is A, which means that the first statement alone is sufficient while second statement alone is not.]]>

= \(\frac{100}{(100/60 + 2/6)}\)

= 50

Option C

]]>

= \(\frac{100}{(100/60 + 2/6)}\)

= 50

Option C]]>

Hi! If the question asked : What is the number of integers from 1 to 1000, inclusive that are not divisible by 11 AND by 35? then the only difference in arriving at the answer would be to find out the multiples of 11 & 35 and subtract that from 1,000, correct?..Thank you in advance.

Yes. In this case the answer would be 1000 - 2 = 998.

]]>

Hi! If the question asked : What is the number of integers from 1 to 1000, inclusive that are not divisible by 11 AND by 35? then the only difference in arriving at the answer would be to find out the multiples of 11 & 35 and subtract that from 1,000, correct?..Thank you in advance.

Yes. In this case the answer would be 1000 - 2 = 998.]]>

Bunuel wrote:

Official Solution:

We should understand the following two things:

1. The probability of selecting any\(n\) numbers from the set is the same. Why should any subset of\(n\) numbers have higher or lower probability of being selected than some other subset of\(n\) numbers? Probability doesn't favor any particular subset.

2. Now, consider that the subset selected is\(\{x_1, \ x_2, \ ..., \ x_n\}\) , where\(x_1 \lt x_2 \lt ... \lt x_n\) . We can select this subset of numbers in

We should understand the following two things:

1. The probability of selecting any\(n\) numbers from the set is the same. Why should any subset of\(n\) numbers have higher or lower probability of being selected than some other subset of\(n\) numbers? Probability doesn't favor any particular subset.

2. Now, consider that the subset selected is\(\{x_1, \ x_2, \ ..., \ x_n\}\) , where\(x_1 \lt x_2 \lt ... \lt x_n\) . We can select this subset of numbers in

...

]]>

Bunuel wrote:

Official Solution:

We should understand the following two things:

1. The probability of selecting any\(n\) numbers from the set is the same. Why should any subset of\(n\) numbers have higher or lower probability of being selected than some other subset of\(n\) numbers? Probability doesn't favor any particular subset.

2. Now, consider that the subset selected is\(\{x_1, \ x_2, \ ..., \ x_n\}\) , where\(x_1 \lt x_2 \lt ... \lt x_n\) . We can select this subset of numbers in

We should understand the following two things:

1. The probability of selecting any\(n\) numbers from the set is the same. Why should any subset of\(n\) numbers have higher or lower probability of being selected than some other subset of\(n\) numbers? Probability doesn't favor any particular subset.

2. Now, consider that the subset selected is\(\{x_1, \ x_2, \ ..., \ x_n\}\) , where\(x_1 \lt x_2 \lt ... \lt x_n\) . We can select this subset of numbers in

...]]>

Hi karishma,

yes, it would be infinite. But i didnot understand the OA of this problem

Please refer the attached screenshot of the problem taken from Veritas Prep mock.

Please let me know if i have missed something!

Let me check with HQ and get back.

]]>

Hi karishma,

yes, it would be infinite. But i didnot understand the OA of this problem

Please refer the attached screenshot of the problem taken from Veritas Prep mock.

Please let me know if i have missed something!

Let me check with HQ and get back.]]>

f(x+1) > f(x), so the equation become

x+1/x+2 > x/x+1

let x =1

2/3 > 1/2 answer is yes

x= -3

-3+1/-3+2 > -3/-3+1

-2/-1 > -3/-2 i.e. 2> 3/2 yes

what x=-2 solution is not defined, how we deal with this case

]]>

f(x+1) > f(x), so the equation become

x+1/x+2 > x/x+1

let x =1

2/3 > 1/2 answer is yes

x= -3

-3+1/-3+2 > -3/-3+1

-2/-1 > -3/-2 i.e. 2> 3/2 yes

what x=-2 solution is not defined, how we deal with this case]]>

Thanks Karishma. Great post..

I was under the impression that when we say |X| < a, we get two options

x<a OR X >=-a..

How does the equal to sign work? Is the same sign preserved when the modulus sign is opened in both cases?

Another eq:

|X| <= a

X <=a OR X>-a... Will the it be >=-a ?? When does the equal to sign come..

In general I am confused about when we open the modulus, how does the equal to sign come in for both the positive and negative cases.. Any explanation

...

]]>

Thanks Karishma. Great post..

I was under the impression that when we say |X| < a, we get two options

x<a OR X >=-a..

How does the equal to sign work? Is the same sign preserved when the modulus sign is opened in both cases?

Another eq:

|X| <= a

X <=a OR X>-a... Will the it be >=-a ?? When does the equal to sign come..

In general I am confused about when we open the modulus, how does the equal to sign come in for both the positive and negative cases.. Any explanation

...]]>

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.

]]>

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.]]>

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.

]]>

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.]]>

Joel sailed for 3 hours at a speed of 20 miles per hour, then for 6 hours at 30 miles per hour and finally, 1 more hour at 40 miles per hour. What was the average speed of Joel during the whole sail?

A. 25

B. 27.5

C. 28

D. 30

E. 32

Hi,

The approach above by everyone is one generally used..

However another way to look at it is by Weighted Average, which is very useful if mastered..

Let's look at average of 20 and 40....

3 units of 20 and 1 unit of 40... avg= 20+(40-20)*1/(3+1)=20+20*1/4=25...

NOW

...

]]>

Joel sailed for 3 hours at a speed of 20 miles per hour, then for 6 hours at 30 miles per hour and finally, 1 more hour at 40 miles per hour. What was the average speed of Joel during the whole sail?

A. 25

B. 27.5

C. 28

D. 30

E. 32

Hi,

The approach above by everyone is one generally used..

However another way to look at it is by Weighted Average, which is very useful if mastered..

Let's look at average of 20 and 40....

3 units of 20 and 1 unit of 40... avg= 20+(40-20)*1/(3+1)=20+20*1/4=25...

NOW

...]]>

abhimahna wrote:

Bunuel wrote:

What is the lowest possible common multiple of 2 distinct integers, each greater than 67?

A. 68

B. 69

C. 136

D. 68^2

E. 68·69

A. 68

B. 69

C. 136

D. 68^2

E. 68·69

Answer should be A.

in order to get the lowest LCM, we have to take the first number as 68 and the next number as its multiple.

So, I can take 68 and 136 as two distinct numbers,such that Lowest LCM = 68. /quote]

seems answer to be C

Lcm of 68 &136=136

...

]]>

abhimahna wrote:

Bunuel wrote:

What is the lowest possible common multiple of 2 distinct integers, each greater than 67?

A. 68

B. 69

C. 136

D. 68^2

E. 68·69

A. 68

B. 69

C. 136

D. 68^2

E. 68·69

Answer should be A.

in order to get the lowest LCM, we have to take the first number as 68 and the next number as its multiple.

So, I can take 68 and 136 as two distinct numbers,such that Lowest LCM = 68. /quote]

seems answer to be C

Lcm of 68 &136=136

...]]>

D = # of dolls

Use the following formulas:

360/L-1 = D+5

360/L = D

You'll eventually get it down to the following:

5L^2 -5L = 360

(L^2 -L) = 72

L^2 -L -72 = 0

(L+8)(L-9) = 0

L = -8 or 9

]]>

D = # of dolls

Use the following formulas:

360/L-1 = D+5

360/L = D

You'll eventually get it down to the following:

5L^2 -5L = 360

(L^2 -L) = 72

L^2 -L -72 = 0

(L+8)(L-9) = 0

L = -8 or 9]]>

Abby --> (j/3)-k+3k

Bill --> (j/3)+k-2k

Carla --> (j/3)+2k-3k

Lastly, we find out Abby has J/2, so we set her amount equal to this and solve.

(j/3)-k+3k =(j/2)

j/6 = 2k

j = 12k

]]>

Abby --> (j/3)-k+3k

Bill --> (j/3)+k-2k

Carla --> (j/3)+2k-3k

Lastly, we find out Abby has J/2, so we set her amount equal to this and solve.

(j/3)-k+3k =(j/2)

j/6 = 2k

j = 12k]]>

H represent those portfolios holding Hatsopoulos stocks

M represent those portfolios holding McQuarrie stocks

35% hold H =>\(z+x = 35\)

40% hold M and do not hold H => y = 40

15% hold H and not M => z = 15

We have , x =20

\(x+y+z = 20 + 40 + 15 = 75\)

There are 25% portfolios holding neither H nor M.

Portfolios that do not hold M =\(z + (neither H nor M)\)

=\(15 + 25\)

...

Attachments

sets_gmc.jpg [ 8.83 KiB | Viewed 79 times ]

]]>

H represent those portfolios holding Hatsopoulos stocks

M represent those portfolios holding McQuarrie stocks

35% hold H =>\(z+x = 35\)

40% hold M and do not hold H => y = 40

15% hold H and not M => z = 15

We have , x =20

\(x+y+z = 20 + 40 + 15 = 75\)

There are 25% portfolios holding neither H nor M.

Portfolios that do not hold M =\(z + (neither H nor M)\)

=\(15 + 25\)

...

Attachments

sets_gmc.jpg [ 8.83 KiB | Viewed 79 times ]

]]>

A department manager distributed a number of pens, pencils, and pads among the staff in the department, with each staff member receiving x pens, y pencils, and z pads. How many staff members were in the department?

(1) The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.

(2) The manager distributed a total of 18 pens, 27 pencils, and 36pads.

[Reveal] Spoiler:

ANSWER I DID:

BOTH statements TOGETHER are sufficient, but neither statement alone is sufficient.

As per OG12:

(1) Each of 10 staff members could have received 2 pens, 3 pencils, and 4 pads, or each of 20 staff members could have received 2 pens, 3 pencils, and 4 pads; NOT sufficient. [Agree]

(2) There could have been 1 staff member who received 18 pens, 27 pencils, and 36 pads, or 3 staff members each of whom received 6 pens, 9 pencils, and 12 pads; NOT sufficient.[Agree]

Assuming both (1) and (2), use the fact that 18:27:36 is equivalent to both 6:9:12 and 2:3:4 to obtain diff erent possibilities for the number of staff . Each of 3 staff members could have received 6 pens, 9 pencils, and 12 pads, or each of 9 staff members could have received 2 pens, 3 pencils, and 4 pads.

Now Here I defer. As per Point 1, its already shown that the ratio is ratio 2:3:4. So, we can clearly choose the staff number is 9.

Can anybody please help me to understand where I am making the mistake in this question?

BOTH statements TOGETHER are sufficient, but neither statement alone is sufficient.

As per OG12:

(1) Each of 10 staff members could have received 2 pens, 3 pencils, and 4 pads, or each of 20 staff members could have received 2 pens, 3 pencils, and 4 pads; NOT sufficient. [Agree]

(2) There could have been 1 staff member who received 18 pens, 27 pencils, and 36 pads, or 3 staff members each of whom received 6 pens, 9 pencils, and 12 pads; NOT sufficient.[Agree]

Assuming both (1) and (2), use the fact that 18:27:36 is equivalent to both 6:9:12 and 2:3:4 to obtain diff erent possibilities for the number of staff . Each of 3 staff members could have received 6 pens, 9 pencils, and 12 pads, or each of 9 staff members could have received 2 pens, 3 pencils, and 4 pads.

Now Here I defer. As per Point 1, its already shown that the ratio is ratio 2:3:4. So, we can clearly choose the staff number is 9.

Can anybody please help me to understand where I am making the mistake in this question?

...

]]>

A department manager distributed a number of pens, pencils, and pads among the staff in the department, with each staff member receiving x pens, y pencils, and z pads. How many staff members were in the department?

(1) The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.

(2) The manager distributed a total of 18 pens, 27 pencils, and 36pads.

[Reveal] Spoiler:

ANSWER I DID:

BOTH statements TOGETHER are sufficient, but neither statement alone is sufficient.

As per OG12:

(1) Each of 10 staff members could have received 2 pens, 3 pencils, and 4 pads, or each of 20 staff members could have received 2 pens, 3 pencils, and 4 pads; NOT sufficient. [Agree]

(2) There could have been 1 staff member who received 18 pens, 27 pencils, and 36 pads, or 3 staff members each of whom received 6 pens, 9 pencils, and 12 pads; NOT sufficient.[Agree]

Assuming both (1) and (2), use the fact that 18:27:36 is equivalent to both 6:9:12 and 2:3:4 to obtain diff erent possibilities for the number of staff . Each of 3 staff members could have received 6 pens, 9 pencils, and 12 pads, or each of 9 staff members could have received 2 pens, 3 pencils, and 4 pads.

Now Here I defer. As per Point 1, its already shown that the ratio is ratio 2:3:4. So, we can clearly choose the staff number is 9.

Can anybody please help me to understand where I am making the mistake in this question?

BOTH statements TOGETHER are sufficient, but neither statement alone is sufficient.

As per OG12:

(1) Each of 10 staff members could have received 2 pens, 3 pencils, and 4 pads, or each of 20 staff members could have received 2 pens, 3 pencils, and 4 pads; NOT sufficient. [Agree]

(2) There could have been 1 staff member who received 18 pens, 27 pencils, and 36 pads, or 3 staff members each of whom received 6 pens, 9 pencils, and 12 pads; NOT sufficient.[Agree]

Assuming both (1) and (2), use the fact that 18:27:36 is equivalent to both 6:9:12 and 2:3:4 to obtain diff erent possibilities for the number of staff . Each of 3 staff members could have received 6 pens, 9 pencils, and 12 pads, or each of 9 staff members could have received 2 pens, 3 pencils, and 4 pads.

Now Here I defer. As per Point 1, its already shown that the ratio is ratio 2:3:4. So, we can clearly choose the staff number is 9.

Can anybody please help me to understand where I am making the mistake in this question?

...]]>

In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors?

A. 2

B. 3

C. 5

D. 6

E. 8

We are given that N is a positive integer less than 200, and 14N/60 is an integer, and we need to determine the number of different positive prime factors of N. Let’s begin by simplifying 14N/60.

14N/60 = 7N/30

In order for 7N/30 to be an integer, N must be divisible by 30. In other words, N must be a multiple of 30. The multiples of 30 less than

...

]]>

In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors?

A. 2

B. 3

C. 5

D. 6

E. 8

We are given that N is a positive integer less than 200, and 14N/60 is an integer, and we need to determine the number of different positive prime factors of N. Let’s begin by simplifying 14N/60.

14N/60 = 7N/30

In order for 7N/30 to be an integer, N must be divisible by 30. In other words, N must be a multiple of 30. The multiples of 30 less than

...]]>

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.

]]>

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 \(x^2 + bx +c = 0\)

Then, (x + p)(x + q) = 0

Therefore

pq = c

p + q = b

The roots of the quadratic equation will be -p and -q.

The question is asking about the product of the roots, meaning (-p)(-q) = ?

This is equal to c = ?, which in turn is equal to pq = ?

- Statement 1: Insufficient, since it only provides -p = 3 or -q = 3

- Statement 2: Sufficient.

OA = B

]]>

If \(x^2 + bx +c = 0\)

Then, (x + p)(x + q) = 0

Therefore

pq = c

p + q = b

The roots of the quadratic equation will be -p and -q.

The question is asking about the product of the roots, meaning (-p)(-q) = ?

This is equal to c = ?, which in turn is equal to pq = ?

- Statement 1: Insufficient, since it only provides -p = 3 or -q = 3

- Statement 2: Sufficient.

OA = B]]>

Mount Washington, in the White Mountains of northern New England, routinely sees some of the coldest temperatures and highest winds in the United States each year

]]>

Mount Washington, in the White Mountains of northern New England, routinely sees some of the coldest temperatures and highest winds in the United States each year]]>

A retailer set the tag price of an item at $200. On a certain public holiday, the retailer set a 20% discount on the tag price, thinking that he will still make a profit equal to 25% of the price he had originally paid for the item. How much did the retailer originally pay for the item?

A. $96

B. $120

C. $128

D. $144

E. $160

After giving a discount of 20% sales price will be 0.8*200=160

Purchase price+0.25*purchase price=160

1.25*purchase price=160

Purchase price= 160/1.25

160*4/5= 128

Hence

...

]]>

A retailer set the tag price of an item at $200. On a certain public holiday, the retailer set a 20% discount on the tag price, thinking that he will still make a profit equal to 25% of the price he had originally paid for the item. How much did the retailer originally pay for the item?

A. $96

B. $120

C. $128

D. $144

E. $160

After giving a discount of 20% sales price will be 0.8*200=160

Purchase price+0.25*purchase price=160

1.25*purchase price=160

Purchase price= 160/1.25

160*4/5= 128

Hence

...]]>