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PS Expert - Math Revolution: Ask Me Anything about GMAT PS 21 Sep 2020, 17:30
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Ask me Anything about GMAT Problem Solving


Hello, I am Max Lee, Founder and Lead Math Tutor at Math Revolution.

We have over 9,000 posts and over 10,000 Kudos. This topic is a new feature on the PS Forum and a way for you to directly interact with our math team and ask anything about the PS, e.g. if you want a certain concept explained or have a particular question you want us to address, this is the place to post a link to it or your question. I intend to have this thread be as an "Everything You Need to Know about PS" type of thread. I will keep updating this post with links and resources that are helpful for the PS. Meanwhile, you can ask me anything ;-)


Other discussions you may be interested in:



We will be posting new questions in this topic regularly - check it out for some new material!
Thank you all - good luck on the GMAT and look forward to seeing you in the PS forum!
- Max Lee.
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PS Expert - Math Revolution: Ask Me Anything about GMAT PS Updated on: 07 Oct 2020, 12:30
Originally posted by MathRevolution on 06 Oct 2020, 02:37.
Last edited by MathRevolution on 07 Oct 2020, 12:30, edited 1 time in total.
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(Integers) If m, n, p, and q are distinct positive integers, greater than 1 such that mnpq = 660 and m<n<p<q, how many possible combinations of values exist for m, n, p, and q?

A) Two
B) Three
C) Four
D) Five
E) Seven
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PS Expert - Math Revolution: Ask Me Anything about GMAT PS 07 Oct 2020, 23:25
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(Integers) If m, n, p, and q are distinct positive integers, greater than 1 such that mnpq = 660 and m<n<p<q, how many possible combinations of values exist for m, n, p, and q?

A) Two
B) Three
C) Four
D) Five
E) Seven
Show more


is the answer 4?
660=11*2*2*3*5
1st combination=3<4<5<11
2nd combination=1<3<5<44
3rd combination=1<5<11<12
4rth combination=1<4<11<15
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PS Expert - Math Revolution: Ask Me Anything about GMAT PS 07 Oct 2020, 12:23
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(Functions): If 2f (x) + 3f (−x) = 2x − 4, what is the value of 5f (1)?

A) 14/5
B) -2
C) 14
D) -14/5
E) -14
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PS Expert - Math Revolution: Ask Me Anything about GMAT PS 11 Oct 2020, 12:19
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(Functions): If 2f (x) + 3f (−x) = 2x − 4, what is the value of 5f (1)?

A) 14/5
B) -2
C) 14
D) -14/5
E) -14
Show more


Thank you for your replies GMAT Club members. GMAT quant is based on logic, tricks, and quick approaches. Always try to find a quick approach to solve any PS or a DS question. We apply the IVY approach for PS and Variable Approach for DS.


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

Substituting x = 1 in equation (1)

2f(1) + 3f(-1) = 2(1) – 4 =2 – 4= -2

2f(1) + 3f(-1) = -2--------- equation (2)

Substituting x = -1 in equation (1)

2f(-1) + 3f(1) = 2(-1) – 4 = -2 – 4 = -6

2f(-1) + 3f(1) = -6--------- equation (3)

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

4f(1) + 6f(-1) = -4--------- equation (4)


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

9f(1) + 6f(-1) = -18--------- equation (5)

Subtracting Eqn(5) - Eqn(4)

=> 5f(1) = -14

=> f(1) = \(\frac{-14}{5}\)

D is the correct answer.

Answer D
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PS Expert - Math Revolution: Ask Me Anything about GMAT PS 11 Oct 2020, 12:20
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(Integers) If m, n, p, and q are distinct positive integers, greater than 1 such that mnpq = 660 and m<n<p<q, how many possible combinations of values exist for m, n, p, and q?

A) Two
B) Three
C) Four
D) Five
E) Seven
Show more

Thank you for your replies GMAT Club members. GMAT quant is based on logic, tricks, and quick approaches. Always try to find a quick approach to solve any PS or a DS question. We apply the IVY approach for PS and Variable Approach for DS.


Solution: Let us find the prime factors of 660.

660 can be written as 660 = 2 * 2 * 3 * 5 * 11.

We have an extra ‘2’ and this can be combined with other factors to generate different values.

Also, considering all other factors than ‘2’, we may combine to generate different values for m, n, p, and q.

Attachment:
Possible Combinations.jpg
Possible Combinations.jpg [ 22.3 KiB | Viewed 14310 times ]

Therefore, we have ‘4’ possible combinations.

C is the correct answer.

Answer C.
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PS Expert - Math Revolution: Ask Me Anything about GMAT PS 14 Oct 2020, 04:40
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(PS)- If the speed limit along a 20-mile section of rail track is reduced from 40 miles per hour to 30 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) 3
B) 5
C) 8
D) 10
E) 12
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PS Expert - Math Revolution: Ask Me Anything about GMAT PS 17 Oct 2020, 00:57
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(PS)- If the speed limit along a 20-mile section of rail track is reduced from 40 miles per hour to 30 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) 3
B) 5
C) 8
D) 10
E) 12
Show more


Solution: Always apply the IVY approach to solve PS questions accurately thus saving time.

Speed * Time = Distance

Length of the section = 20 miles

Original speed limit: 40 miles per hour

Thus, time is taken to cover this distance = \(\frac{20}{40}= \frac{1}{2}\)

New speed limit: 30 miles per hour

Thus, time is taken to cover this distance = \(\frac{20}{30} = \frac{2}{3}\)

Thus, the required difference between the time durations is given = \(\frac{2}{3} - \frac{1}{2} \) = \(\frac{1}{6}\) hours

=> \(\frac{1}{6} * 60 = 10\) minutes

D is the correct answer.

Answer D.
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PS Expert - Math Revolution: Ask Me Anything about GMAT PS 17 Oct 2020, 01:04
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(Statistics) Heights of citizens 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 19 Oct 2020, 11:28
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(Statistics) Heights of citizens 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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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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PS Expert - Math Revolution: Ask Me Anything about GMAT PS 19 Oct 2020, 11:31
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A ball thrown up in the air is at a height of h feet, t seconds after it was thrown, where \(h = −3(t − 10)^2 + 250\). What is the height of the ball once it reached its maximum height and then descended for 7 seconds

A) 96 feet
B) 103 feet
C) 164 feet
D) 223 feet
E) 250 feet

Solution: We know that \(h = −3(t − 10)^2 + 250\)

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

For ‘h’ to be maximum, \(−3(t − 10)^2\) should be maximum. Since \((t − 10)^2\) is a perfect square, therefore, \((t − 10)^2\) ≥ 0.

But, \(−3(t − 10)^2\) will be ≤ 0 [By the property of reverse inequality]

So, for ‘h’ to be maximum \(−3(t − 10)^2\)= 0

=> \(−3(t − 10)^2\) = 0

=> \((t − 10)^2\) = 0

=> (t − 10) = 0

=> t = 10.

‘7’ seconds after ball has reached maximum height ‘h’ at t = 10 + 7 = 17.

=> \(h = −3(t − 10)^2 + 250\)

=> \(h = −3(17 − 10)^2 + 250\)

=> h = −3 * 49 + 250

=> h = -147 + 250

=> h = 103 feet

Answer B
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Hey, got this problem on one of my practice tests and cannot figure it out or understand the explanation given... Can someone break this down? Cheers and happy studying

† and ¥ represent nonzero digits, and (†¥)² - (¥†)² is a perfect square. What is that perfect square?

(a) 121
(b) 361
(c) 576
(d) 961
(e) 1089
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Hi, this question looks easy but so difficult for me. Please help to solve this one, thank you :)
-----
Raymond purchased a package of ground beef at a cost of $1.98 per pound. If, for the same amount of money, Raymond could have purchased a piece of steak that weighed 40 percent less than the package of ground beef, what was the cost per pound of the steak?

A 4.95, B 4.20, C 3.6, D 3.3, E 3.10
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Hi, this question looks easy but so difficult for me. Please help to solve this one, thank you :)
-----
Raymond purchased a package of ground beef at a cost of $1.98 per pound. If, for the same amount of money, Raymond could have purchased a piece of steak that weighed 40 percent less than the package of ground beef, what was the cost per pound of the steak?

A 4.95, B 4.20, C 3.6, D 3.3, E 3.10
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This question is discussed here: https://gmatclub.com/forum/raymond-purc ... 07469.html Hope it helps.

P.S. Please read carefully our posting rules: https://gmatclub.com/forum/rules-for-po ... 33935.html Thank you,
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Hey, got this problem on one of my practice tests and cannot figure it out or understand the explanation given... Can someone break this down? Cheers and happy studying

† and ¥ represent nonzero digits, and (†¥)² - (¥†)² is a perfect square. What is that perfect square?

(a) 121
(b) 361
(c) 576
(d) 961
(e) 1089
Show more

I broke the question into:
(10† + ¥)² - (10¥ + †)²
opening up the brackets gives
(100†² + 20†¥ + ¥²) - (100¥² + 20†¥ - †²)
Simplifying further gives
100{†²- ¥²} + {¥² - †²}
factoring the second bracket with -1
100{†²- ¥²} - {†²-¥²}
{†²- ¥²}(100 -1)
{†²- ¥²} 99
Hence the number must be a multiple of 99.

In the Answer options 1089 divides 99 to give 11.
Answer E is the correct choice.

(Kindly check if there are any errors in there)

Posted from my mobile device
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Que: A fitness club has 40 male and 10 female members. The average (arithmetic mean) age of all of the members is 24 years. If the average age of the male members was 22 years, which of the following is the average age, in years, of the female members?

(A) 25
(B) 30
(C) 32
(D) 34
(E) 26
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Que: A number 4p25q is divisible by 4 and 9; where p and q are the thousands and units digits, respectively. What is the minimum value of \(\frac{p}{ q}\)

(A) \(\frac{1}{8}\)
(B) \(\frac{1}{7}\)
(C) \(\frac{1}{6}\)
(D) \(\frac{2}{5}\)
(E) \(\frac{5}{2}\)
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Que: A fitness club has 40 male and 10 female members. The average (arithmetic mean) age of all of the members is 24 years. If the average age of the male members was 22 years, which of the following is the average age, in years, of the female members?

(A) 25
(B) 30
(C) 32
(D) 34
(E) 26
Show more

Solution: We have 40 males and 10 females. Hence, total members are: 40 + 10 = 50

Let the average age, in years, of the female members be x, then we get

=> \(\frac{(40 * 22 + 10 * x)}{(40+10)}\)=24

=> 40 * 22 + 10x = 24 * 50

=> 880 + 10x = 1,200

10x=1200 – 880 = 320 which means that the sum of the ages of 10 female members is 320

Also, we get 10x = 320, x = \(\frac{320}{10}\) = 32, which means that the average age of these 10 female members is = 32.

C is the correct answer.

Answer C
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PS Expert - Math Revolution: Ask Me Anything about GMAT PS Updated on: 07 Nov 2020, 03:33
Originally posted by MathRevolution on 07 Nov 2020, 03:23.
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Que: A number 4p25q is divisible by 4 and 9; where p and q are the thousands and units digits, respectively. What is the minimum value of \(\frac{p}{ q}\)

(A) \(\frac{1}{8}\)
(B) \(\frac{1}{7}\)
(C) \(\frac{1}{6}\)
(D) \(\frac{2}{5}\)
(E) \(\frac{5}{2}\)
Show more

Solution: Divisibility property of ‘4’: A number is divisible by ‘4’ when its last two digits are divisible by ‘4’.

Therefore, ‘5q’ is divisible by 4.

So, the possible values of ‘q’ are 2 or 6 [both 52 and 56 are divisible by 4]

Divisibility property of ‘9’: A number is divisible by ‘9’ when the sum of all its digits is divisible by ‘9’

Therefore, 4 + p + 2 + 5 + q = 11 + p + q.

So, the possible values of ‘p’ and ‘q’ so that 11 + p + q is divisible by ‘9’are:

For q = 2

=> 11 + p + 2 = 13 + p

=>‘p’ should be 5 [since 13 + 5 = 18 is divisible by 9]

For q = 6

=> 11 + p + 6 = 17 + p
=> ‘p’ should be 1 [since 17 + 1 = 18 is divisible by 9]

So, we have two pairs for ‘p’ and ‘q’: (5, 2) and (1,6)

=> Minimum value of \(\frac{p}{q}\) = \(\frac{1}{6}\)

C is the correct answer.

Answer C
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Que: A chemical evaporates out of a beaker at the rate of x liters for every y minutes. If the chemical costs 25 dollars per liter, what is the cost, in dollars, of the amount of the chemical that will evaporate in z minutes?

(A) \(\frac{25}{yz}\)

(B) \(\frac{xz}{25q}\)

(C) \(\frac{25y}{xz}\)

(D) \(\frac{25xz}{y}\)

(E) \(\frac{25yz}{x}\)
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