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PS Expert - Math Revolution: Ask Me Anything about GMAT PS

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MathRevolution
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post   13 Jun 2021, 22:03
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MathRevolution wrote:
Que: Box P and Box Q each contain many red balls and white balls. All of the white balls have the same radius. The radius of each white ball is 6 inches less than the average radius of the balls in Box P and 3 inches greater than the average radius of the balls in Box Q. What is the difference between the average (arithmetic mean) radius, in inches, of the balls in Box P and of the balls in Box Q?

(A) 3
(B) 4
(C) 6
(D) 8
(E) 9


Solution: Let the radius of each white ball = x inches.

Each green ball is 6 inches less than the average radius of the balls in Box P.

Thus, the average radius of balls in Box P = (x + 6) inches.

Also, each white ball is 3 inches greater than the average radius of the balls in Box Q.

Thus, the average radius of balls in Box Q = (x − 3) inches.

Thus, the required difference = ((x + 6) − (x − 3)) = 9 inches.

Therefore, E is the correct answer.

Answer E
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post   13 Jun 2021, 22:19
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MathRevolution wrote:
Que: A juice manufacturer has 2,000 liters of mango pulp in stock, 40 percent of which is water. If the manufacturer adds another 1,000 liters of mango pulp of which 50 percent is water, what percent, by volume, of the manufacturer’s mango pulp contains water?

(A) 10%
(B) 16.67%
(C) 26.67%
(D) 43.33%
(E) 65%


Solution: The resultant percentage will be the weighted average of the percentages of the above two stocks.

=> \(\frac{40}{100}\) = 0.4

=> \(\frac{50}{100}\) = 0.5

=> \(\frac{[2,000 * 0.4] + [1,000 * 0.5 ] }{ [2,000 + 1,000]}\)

=> \(\frac{(800 + 500) }{ (3,000)} * 100\)

=> \((\frac{1,300}{3,000}) * 100 => 43.33%\)

Therefore, D is the correct answer.

Answer D
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post   13 Jun 2021, 22:28
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Que: 40, 50, 60, 70, 80, 90, 100, 110, 120, 130

The list above shows the scores of 10 students obtained on a scheduled test. If the standard deviation of the 10 scores is 30.28, how many of the scores are greater than one standard deviation above the mean of the 10 scores?

(A) None
(B) One
(C) Two
(D) Three
(E) Four
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post   13 Jun 2021, 22:30
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Que: If the speed limit along a 30-mile section of rail track is reduced from 30 miles per hour to 15 miles per hour. Approximately how many minutes more will it take a rail to travel along this section with the new speed limit than it would have taken at the old speed limit?

A) 30
B) 40
C) 45
D) 60
E) 120
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post   14 Jun 2021, 22:30
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MathRevolution wrote:
Que: 40, 50, 60, 70, 80, 90, 100, 110, 120, 130

The list above shows the scores of 10 students obtained on a scheduled test. If the standard deviation of the 10 scores is 30.28, how many of the scores are greater than one standard deviation above the mean of the 10 scores?

(A) None
(B) One
(C) Two
(D) Three
(E) Four


Solution: Question asks the number of scores > (Mean + S.D.)

=> Mean = \(\frac{(40 + 50 + 60 + 70 + 80 + 90 + 100 + 110 + 120 + 130) }{ 10} = \frac{850 }{ 10} = 85\)

=> S.D. = 30.28. Thus,

=> Mean + S.D. = 85 + 30.28 = 115.28

It is clear that three scores (120 and 130) are greater than 115.28.

Therefore, C is the correct answer.

Answer C
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post   14 Jun 2021, 22:35
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MathRevolution wrote:
Que: If the speed limit along a 30-mile section of rail track is reduced from 30 miles per hour to 15 miles per hour. Approximately how many minutes more will it take a rail to travel along this section with the new speed limit than it would have taken at the old speed limit?

A) 30
B) 40
C) 45
D) 60
E) 120



Solution: Speed * Time = Distance

Length of the section = 30 miles

Original speed limit: 30 miles per hour

Thus, time taken to cover this distance = \(\frac{30}{30}\) = 1 hour

New speed limit: 15 miles per hour

Thus, time taken to cover this distance = \(\frac{30}{15}\) = 2 hour

Thus, the required difference between the time durations is given = 2-1 = 1 hour = 1 * 60 = 60 minutes

D is the correct answer.

Answer D
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post   14 Jun 2021, 22:43
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Que: Heights of trees in a large population have a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is greater than (m − d)?

A) 66%
B) 50%
C) 67%
D) 84%
E) 34%
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PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post   14 Jun 2021, 23:55
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Que: A ball thrown up in the air is at a height of h feet, t seconds after it was thrown, where \(h = −5(t − 20)^2 + 180\). What is the height of the ball once it reached its maximum height and then descended for 5 seconds?

A) 55 feet
B) 105 feet
C) 190 feet
D) 200 feet
E) 255 feet
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post   16 Jun 2021, 20:44
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MathRevolution wrote:
Que: Heights of trees in a large population have a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is greater than (m − d)?

A) 66%
B) 50%
C) 67%
D) 84%
E) 34%



Solution: We know that the distribution is symmetric about the mean. This is the concept of Normal distribution.

Thus, the percent of the distribution equidistant from the mean on either side of it is the same.

Let the percent of the distribution less than (m - d) be x%. Thus, the percent of the distribution more than (m + d) is also x%.

Thus, we have

=> x% + 68% + x% = 100%

=> 2x = 32%, x=16%

Thus, the percent of the distribution greater than (m − d) = 100% - x% =100% - 16% = 84%.

D is the correct answer.

Answer D
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post   16 Jun 2021, 20:53
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MathRevolution wrote:
Que: A ball thrown up in the air is at a height of h feet, t seconds after it was thrown, where \(h = −5(t − 20)^2 + 180\). What is the height of the ball once it reached its maximum height and then descended for 5 seconds?

A) 55 feet
B) 105 feet
C) 190 feet
D) 200 feet
E) 255 feet



Solution: We know that \(h = −5(t − 20)^2 + 180\).

We will first find the value for ‘t’ for which ‘h’ will be maximum.

For ‘h’ to be maximum, \(−5(t − 20)^2\) should be maximum. Since (t − 20)^2 is a perfect square, therefore, \((t − 20)^2\) ≥ 0.

But, \(−5(t − 20)^2\) will be ≤ 0 [By the property of reverse inequality]

So, for ‘h’ to be maximum \(−5(t − 20)^2 = 0\)

=> \(−5(t − 20)^2 = 0\)

=> \((t − 20)^2 = 0\)

=> (t − 20) = 0

=> t = 20.

‘5’ seconds after ball has reached maximum height ‘h’ at t = 20 + 5 = 25.

=> \(h = −5(25 − 20)^2 + 180\)

=> \(h = −5(5)^2 + 180\)

=> h = −5 * 25 + 180

=> h = -125 + 180

=> h = 55 feet

A is the correct answer.

Answer A
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post   16 Jun 2021, 21:03
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Que: A set is such that if m is in the set, m + 3 is also in the set. If −2 is in the set, which of the following is also in the set?

I. −2
II. 1
III. 4

(A) Only I
(B) Only II
(C) Only I and II
(D) Only II and III
(E) I, II, and III
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post   17 Jun 2021, 21:50
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MathRevolution wrote:
Que: A set is such that if m is in the set, m + 3 is also in the set. If −2 is in the set, which of the following is also in the set?

I. −2
II. 1
III. 4

(A) Only I
(B) Only II
(C) Only I and II
(D) Only II and III
(E) I, II, and III



Solution: According to the problem: If m is in the set, (m + 3) is also in the set.

However, it does NOT imply that if (m + 3) is in the set, then m must be in the set.

What it does imply is that: If (m + 3) is NOT in the set, m is NOT in the set.

Thus, if we have m = −2 as a member of the set, m + 3 = (-2) + 3 = 1 is also a member of the set. Thus, statement II is correct.

Proceeding in the same way: Since m = 1 is a member of the set, then m + 3 = 1 + 3 = 4 is a member of the set. Thus, statement III is also correct.

Therefore, D is the correct answer.

Answer D
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post   17 Jun 2021, 21:57
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Que: In a class, 80 percent of the boys and 20 percent of the girls play basketball. If 75 percent of all the students play basketball, what is the ratio of the number of girls that did not play basketball to the number of boys who play basketball?

(A) \(\frac{2}{5}\)

(B) \(\frac{5}{2} \)

(C) \(\frac{1}{11} \)

(D) \(\frac{5}{11} \)

(E) \(\frac{13}{11}\)
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post   18 Jun 2021, 22:23
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MathRevolution wrote:
Que: In a class, 80 percent of the boys and 20 percent of the girls play basketball. If 75 percent of all the students play basketball, what is the ratio of the number of girls that did not play basketball to the number of boys who play basketball?

(A) \(\frac{2}{5}\)

(B) \(\frac{5}{2} \)

(C) \(\frac{1}{11} \)

(D) \(\frac{5}{11} \)

(E) \(\frac{13}{11}\)



Solution: Let the number of the boys be 100b and the number of girls is 100g, then we get the total number of students to be 100(b + g).

As we are dealing with percent, according to the IVY approach take ‘100’ as total, and b and g are the initials of the words ‘boys’ and “girls” respectively.

Also this question is applied by the IVY Approach, Each Each Together

=> 80 percent of the boys: \(\frac{60}{100} * 100b = 80b\) (Each)

=> 20 percent of the girls: \(\frac{20}{100} * 100g = 20g\) (Each)

=> 75 percent of all the students: \(\frac{75}{100} * 100(b + g) = 75(b + g)\) (Together)

Then, we get 80b + 20g = 75(b + g) = 75b + 75g.

Rearranging gives us that 80b – 75b = 75g – 20g

=> 5b = 55g, b = 11g.

Ratio of number of girls who did not play basketball : Ratio of number of boys who plays basketball:

=> 80g : 80b = g : b = g : 11g = 1 : 11

=> 1:11

Thus, the ratio of number of girls to the number of boys: 1:11

Therefore, C is the correct answer.

Answer C
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post   18 Jun 2021, 22:32
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Que: A quiz consists of X questions, each of which is to be answered either “Yes”, “No.” or “Don’t know.” What is the least value of X for which the probability is less than 1/300 such that a participant who randomly guesses the answer to each question will be a winner?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post   19 Jun 2021, 22:26
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MathRevolution wrote:
Que: A quiz consists of X questions, each of which is to be answered either “Yes”, “No.” or “Don’t know.” What is the least value of X for which the probability is less than 1/300 such that a participant who randomly guesses the answer to each question will be a winner?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8


Solution: Total questions: X

Total options for each question: 3 [Yes, No, or Don’t know]

Thus, the probability of randomly guessing an answer and getting it correct = 1/3

Thus, the probability of randomly guessing answers to all X questions and getting them correct:

=> \(\frac{1}{3}* \frac{1}{3}* ….. X \)times

=> \((\frac{1}{3})^x\)

=> \((\frac{1}{3})^x < \frac{1}{300}\)

=> \(\frac{1}{3^x} < \frac{1}{300}\)

=> \(3^x > 300\)

For x = 6, 36 = 729, which exceeds 300.

Therefore, C is the correct answer.

Answer C
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post   19 Jun 2021, 22:34
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Que: If 4f (x) - 3f (− x) = 2x − 7, what is the value of f (3)?

A) \(0\)

B) \(\frac{1}{7}\)

C) \(\frac{-43}{7 }\)

D) \(\frac{36}{7}\)

E) \(\frac{43}{7}\)
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post   20 Jun 2021, 22:09
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MathRevolution wrote:
Que: If 4f (x) - 3f (− x) = 2x − 7, what is the value of f (3)?

A) \(0\)

B) \(\frac{1}{7}\)

C) \(\frac{-43}{7 }\)

D) \(\frac{36}{7}\)

E) \(\frac{43}{7}\)


Solution: 4f(x) - 3 f(-x) = 2x - 7 --------- equation (1)

Substituting x = 3 in equation (1)

=> 4f(3) - 3f(-3) = 2(3) - 7

=> 4f(3) - 3f(-3) = -1--------- equation (2)

Substituting x = -3 in equation (1)

=> 4f(-3) - 3f(3) = 2(-3) - 7

=> 4f(-3) - 3f(3) = -13--------- equation (3)

Multiplying equation (2) by ‘4’ we get,

=> 16f(3) - 12f(-3) = -4--------- equation (4)


Multiplying equation (3) by ‘3’ we get,

=> 12f(-3) - 9f(3) = -39--------- equation (5)

Adding Eqn(4) + Eqn(5)

=> 7f(3) = -43

=> f(3) = \(\frac{-43}{7}\)


C is the correct answer.

Answer C
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post   23 Jun 2021, 23:58
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Que: An insurance claim has 150 numbers of pages to be typed, of which 50 were revised only once, 25 were revised twice, and the rest has no revisions. Megan has a typing service agency and charges $8 per page if the page is typed for the first time and $4 per page each time a page is revised. How much does it cost to have the insurance claim printed at Megan’s typing agency?

(A) 600
(B) 900
(C) 1,000
(D) 1,100
(E) 1,200
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post   25 Jun 2021, 22:01
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MathRevolution wrote:
Que: An insurance claim has 150 numbers of pages to be typed, of which 50 were revised only once, 25 were revised twice, and the rest has no revisions. Megan has a typing service agency and charges $8 per page if the page is typed for the first time and $4 per page each time a page is revised. How much does it cost to have the insurance claim printed at Megan’s typing agency?

(A) 600
(B) 900
(C) 1,000
(D) 1,100
(E) 1,200


Solution: Total number of pages = 150

Revised once: 50

Revised twice: 25

Remaining: 150 – (50 + 25) = 75

=> Rate for first typing: $8

=> Rate for first revised: $4

Rate for second revised: $4 + $4 = $8

Total cost = (75 * 8) + (50 * 4) + (25 * 8) = 600 + 200 + 200 = $1,000

Therefore, C is the correct answer.

Answer C
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