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: How to Improve GMAT Quant from Q49 to Q51 - the Ultimate Q51 Quide Overview of GMAT Math Question Types and Patterns on the GMAT 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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MathRevolution

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26 Jun 2021, 04:19

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Que: A shipping company consists of 40 ‘type A’ ships at the beginning of 2010. At the end of each year, starting with 2010, the company retired 5 of the ‘type A’ ships and acquired 8 new ‘type B’ ships. How many years did it take before the number of ‘type A’ planes left in the company was less than 40 percent of the ships?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

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27 Jun 2021, 00:38

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MathRevolution

(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

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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27 Jun 2021, 09:33

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Is the answer 5
2-5-6-11; 3-4-5-11; 3-5-6-11; 2-3-5-22; 2-3-10-11.

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27 Jun 2021, 09:41

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Ans is 4 years
0 yr- 40A+0B
1st yr- 35A+8B
2nd yr- 30A+16B
3rd yr- 25A+24B
4th yr- 20A+32B

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27 Jun 2021, 10:05

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MathRevolution

(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

Answer is -14;
While solving the equation after plugging 1 & -1 to the base equation
we derive
2f(-1)+3f(1)= -6
3f(-1)+2f(1)= -2
from the equation we get f(-1)= 6/5 & f(1)= -14/5
so 5f(1)= -14

MathRevolution

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27 Jun 2021, 21:06

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MathRevolution

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Solution: 40 percent of ships: $\frac{40}{100} * 40 = 16$.

In 2010, Type A ship = 40
Type B ship = 0

In 2011, Type A ship = 40 – 5 = 35
Type B ship = 8

In 2012, Type A ship = 35 – 5 = 30
Type B ship = 8 + 8 = 16

In 2013, Type A ship = 30 – 5 = 25
Type B ship = 24

Therefore, in 4 years, ‘type A’ ship = 25 – 5 = 20 which is 40 percent less than of total ships.

Since Type B ship = 24 + 8 = 32 and $\frac{20}{(20 + 32)} = \frac{20}{52} = 38.46% < 40%.$

Therefore, C is the correct answer.

Answer C

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27 Jun 2021, 21:15

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Que: John sold his car at a loss of 20 percent of the price that he originally paid for the car, and then bought another car at a price of 40 percent less than the price he originally paid for his first car. If he sold the first car for $16,000, what was his net gain, in dollars, for the two transactions?

(A) $3,000
(B) $4,000
(C) $4,800
(D) $16,000
(E) cannot be determined

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Solution: Selling Price of the first car: $16,000.

This was sold at a 20 percent loss. This means C.P. * $\frac{80 }{ 100}$ = 16,000.

C.P. of the first car: $16000 * \frac{100 }{ 80} = 20,000$

C.P. of second car: 40 percent less than the C.P. of first car: $20,000 * \frac{60 }{ 100} = 12,000 $

=> C.P. 1 = 20,000

=> S.P. 1 = 16,000

=> Loss 1 = 20,000 – 16,000 = 4,000

=> C.P. 2 = 12,000

=> Gain in second car: 20,000 – 12,000 = 8,000

Overall gain: 8,000 – 4,000 = 4,000

Therefore, B is the correct answer.

Answer B

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29 Jun 2021, 22:18

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Que: If both $7$ and $3^3$ are factors of $p * 4^4 * 6^2 * 5^4$ , then what is the smallest possible value of p?

(A) 3
(B) 7
(C) 21
(D) 189
(E) 243

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Que: If both $7$ and $3^3$ are factors of $p * 4^4 * 6^2 * 5^4$ , then what is the smallest possible value of p?

(A) 3
(B) 7
(C) 21
(D) 189
(E) 243

Solution: Express the given number $p * 4^4 * 6^2 * 5^4$ in prime factors as $p * 2^8 * 2^2 * 3^2 * 5^4$.

=> For 7 to be the factor it should be contained in it. If we remove p then we don’t have 7. Hence p = 7.

$3^2$ is contained already and hence we need 1 more 3 so that $3^3$ is the factor and hence 3 should also be in p.

=> Thus, smallest value of p = 3 * 7 = 21

Therefore, C is the correct answer.

Answer C

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02 Jul 2021, 20:51

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Que: Find the number of keystrokes required to type numbers from 2 to 1002.

(A) 2,900
(B) 2,901
(C) 3,000
(D) 3,280
(E) 4,000

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Que: Find the number of keystrokes required to type numbers from 2 to 1002.

(A) 2,900
(B) 2,901
(C) 3,000
(D) 3,280
(E) 4,000

Solution: The number range is from 2 to 1002.

=> One digit numbers = 2 to 9 = 8 [Will need 1 key stroke each] = 8 key strokes

=> Two digit numbers = 10 to 99 [Will need 2 key stroke each] = 90 * 2 = 180 key strokes

=> Three digit numbers = 100 to 999 [Will need 3 key stroke each] = 900 * 3 = 2700 key strokes

=> Four digit numbers = 1000 to 1002 [Will need 4 key stroke each] = 3 * 4 = 12 key strokes

=> Total keystrokes = 8 + 180 + 2700 + 12 = 2900

Therefore, A is the correct answer.

Answer A

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Que: Find the number of trailing zeroes after the rightmost non-zero digit in the value of 30!

A) 3
B) 6
C) 7
D) 10
E) 25

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Que: Find the number of trailing zeroes after the rightmost non-zero digit in the value of 30!

A) 3
B) 6
C) 7
D) 10
E) 25

Solution: 30! = 30 * 29 * 28 *………. * 3 * 2 * 1

When ‘5’ is multiplied by an even number, it results in ‘0’.

Numbers in 30! , which has ‘5’ as the factor are: 5, 10, 15, 20, 25, 30

25 will have ‘2’ (5’s). Hence, we have 7 ‘5’s’ and at least 7 even numbers in 30! , which when multiplied by 5 will result in ‘0’.

C is the correct answer.

Answer C.

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Que: Item X attracts a sales tax rate of $1.00 per $30. What is the sales tax rate, as a percent, for item Y that attracts three times as much as the rate for item X?

(A) 0.1%
(B) 1%
(C) 3%
(D) 10%
(E) 30%

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Solution: Tax paid on $30 = $1.00

Thus, a tax, which is three times as much as the above, would be $(1.00 × 3) = $3.00 on $30.

Thus, the tax rate = $\frac{$3.00}{$30} = 0.1 $

Thus, this tax, expressed as a percentage = $0.1 = 1 × \frac{1}{10} = 10%. $

Therefore, D is the correct answer.

Answer D

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Que: A juice manufacturer has 1,800 liters of mango pulp in stock, 30 percent of which is water. If the manufacturer adds another 600 liters of mango pulp of which 30 percent is water, what percent, by volume, of the manufacturer’s mango pulp contains water?

(A) 20%
(B) 25%
(C) 30%
(D) 35%
(E) 40%

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

=> $\frac{[(1,800 * 0.3) + (600 * 0.3)]}{ (1,800 + 600)} * 100$

=> $\frac{(540 + 180) }{ (2,400)} * 100$

=> $(\frac{720}{2,400}) * 100 => 30%$

Therefore, C is the correct answer.

Answer C

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16 Jul 2021, 09:59

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Que: The trader first decreased the selling price of a car by 30 percent and then increased by 30 percent. Which of the following represents the final percent change in the selling price of the bicycle?

(A) 9% less
(B) 0%
(C) 9% more
(D) 91% less
(E) 91% more