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PS Expert - Math Revolution: Ask Me Anything about GMAT PS
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MathRevolution
Math Revolution GMAT Instructor
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Posts: 11851
GMAT 1: 760 Q51 V42
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post  16 Jul 2021, 08:59
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
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MathRevolution
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post  17 Jul 2021, 21:15
MathRevolution wrote:
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



Solution: Let us apply the IVY approach to solve the question. As we are dealing with percentage, then let the original price of a car be $100.

Price after price reduced by 30%: (100 - 30)% of $100

=> \((\frac{70}{100})*$100 = $70\)

Price after the new price increased by 30%: (100 + 30)% of $70

=> \((\frac{130}{100})$70 = $91\)

As the base price is $100, the final price would be 91% of the base price.

Since Percent change = \(\frac{(After - Before)}{Before} * 100\)(%) and $100 (Before) and $91 (After),

We get Percent change = \(\frac{($91 - $100)}{$100} * 100\)(%) =\( \frac{(-9)}{100} * 100\)(%) = -9%

Therefore, A is the correct answer.

Answer A
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MathRevolution
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post  17 Jul 2021, 21:24
Que: An instructor gave the same test to three groups: A, B, and C. The average (arithmetic mean) scores for the three groups were 40, 50, and 60, respectively. The ratio of the numbers of candidates in the A, B, and C groups were 1 : 3: 5, respectively. What was the average score for the three groups combined?

(A) 21.11
(B) 36.66
(C) 50
(D) 54.44
(E) 80
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MathRevolution
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post  19 Jul 2021, 01:16
MathRevolution wrote:
Que: An instructor gave the same test to three groups: A, B, and C. The average (arithmetic mean) scores for the three groups were 40, 50, and 60, respectively. The ratio of the numbers of candidates in the A, B, and C groups were 1 : 3: 5, respectively. What was the average score for the three groups combined?

(A) 21.11
(B) 36.66
(C) 50
(D) 54.44
(E) 80



Solution: Let the number of candidates in groups A, B, and C be 1k, 3k, and 5k, respectively, where ‘k's is a constant of proportionality.

The average (arithmetic mean) scores for the three groups were 40, 50, and 60, respectively. The combined average for the three groups is

=> \(\frac{[ (40 * k) + (50 * 3k) + (60 * 5k)] }{ (k + 3k + 5k)}\)

=> \(\frac{[(40k + 150k + 300k)]}{ (9k)}\)

=> \(\frac{490k }{ 9k} = 54.44\)

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  19 Jul 2021, 01:22
Que: A color “code” is defined as a sequence of four dots arranged in a row. Each dot is colored either “blue” or “green.” How many distinct codes can be formed?

(A) 2
(B) 4
(C) 8
(D) 16
(E) 32
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MathRevolution
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post  19 Jul 2021, 23:28
MathRevolution wrote:
Que: A color “code” is defined as a sequence of four dots arranged in a row. Each dot is colored either “blue” or “green.” How many distinct codes can be formed?

(A) 2
(B) 4
(C) 8
(D) 16
(E) 32



Solution: The first dot can use Blue or Green, the second dot also can use Blue or Green, the third dot also can use Blue or Green and the Fourth dot also can use Blue or Green, so 2 * 2 * 2 * 2 = 16

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  19 Jul 2021, 23:33
Que: Find the number of keystrokes required to type numbers from 1 to 900?

(A) 2,583
(B) 2,589
(C) 2,590
(D) 2,592
(E) 2,593
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post  05 Aug 2021, 20:16
MathRevolution wrote:
Que: Find the number of keystrokes required to type numbers from 1 to 900?

(A) 2,583
(B) 2,589
(C) 2,590
(D) 2,592
(E) 2,593



Solution: The number range is from 1 to 900.

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

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

Three digit numbers = 100 to 900 [Will need 3 key stroke each] = 801 * 3 = 2403 key strokes

Total keystrokes = 9 + 180 + 2403 = 2592

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  05 Aug 2021, 20:25
Que: A book to be reprinted has 300 numbers of pages to be typed, of which 80 were revised only once, 50 were revised twice, and the rest has no revisions. The typing service agency charges $10 per page if the page is typed for the first time and $5 per page each time a page is revised. How much does it cost to have the book reprinted?

(A) 1,500
(B) 1,700
(C) 2,350
(D) 2,500
(E) 3,000
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post  07 Aug 2021, 22:46
MathRevolution wrote:
Que: A book to be reprinted has 300 numbers of pages to be typed, of which 80 were revised only once, 50 were revised twice, and the rest has no revisions. The typing service agency charges $10 per page if the page is typed for the first time and $5 per page each time a page is revised. How much does it cost to have the book reprinted?

(A) 1,500
(B) 1,700
(C) 2,350
(D) 2,500
(E) 3,000


Solution: Total number of pages = 300

=> Revised once: 80

=> Revised twice: 50

=> Remaining: 300 – (80 + 50) = 170

=> Rate for first typing: $10

=> Rate for first revised: $5

=> Rate for second revised: $5 + $5 = $10

=> Total cost = (170 * 10) + (80 * 5) + (50 * 8) = 1700 + 400 + 400 = $2,500

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  07 Aug 2021, 22:51
Que: A pen company manufactures two types of the pen: Pen A and Pen B. The company manufactures 200 ‘type A’ pens at the beginning of 2015. At the end of each year, starting with 2015, the company retired 50 of the ‘type A’ pens and acquired 75 new ‘type B’ pens. How many years did it take before the number of ‘type A’ pens left in the company was less than 50 percent of the pens?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
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MathRevolution
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post  08 Aug 2021, 20:40
MathRevolution wrote:
Que: A pen company manufactures two types of the pen: Pen A and Pen B. The company manufactures 200 ‘type A’ pens at the beginning of 2015. At the end of each year, starting with 2015, the company retired 50 of the ‘type A’ pens and acquired 75 new ‘type B’ pens. How many years did it take before the number of ‘type A’ pens left in the company was less than 50 percent of the pens?

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


Solution: 50 percent of pens: \(\frac{50}{100} * 200 = 100.\)

=> In 2015, type A pen = 200
=> Type B pen = 0

=> In 2016, type A pen = 200 – 50 = 150
=> Type B pen = 75

=> In 2017, type A pen = 150 – 50 = 100
=> Type B pen = 75 + 75 = 150

=> In 2018, type A pen = 100 – 50 = 50
=> Type B pen = 225

Therefore, in 3 years, ‘type A’ pen = 100 – 50 = 50 which is 50 percent less than of total ships.

Therefore, B is the correct answer.

Answer B
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post  08 Aug 2021, 20:46
Que: Charlie sold his car at a profit of 30 percent of the price that he originally paid for the car and then bought another car at a price of 60 percent less than the price he originally paid for his first car. If he sold the first car for $26,000, what was his net gain or loss, in dollars, for the two transactions?

(A) $6,000 gain
(B) $6,000 loss
(C) $8,000 loss
(D) $8,000 gain
(E) $18,000 gain
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post  09 Aug 2021, 20:36
MathRevolution wrote:
Que: Charlie sold his car at a profit of 30 percent of the price that he originally paid for the car and then bought another car at a price of 60 percent less than the price he originally paid for his first car. If he sold the first car for $26,000, what was his net gain or loss, in dollars, for the two transactions?

(A) $6,000 gain
(B) $6,000 loss
(C) $8,000 loss
(D) $8,000 gain
(E) $18,000 gain



Solution: Selling Price of the first car: $26,000

=> This was sold at 30 percent profit. This means C.P. * \(\frac{130 }{ 100}\) = 26,000.

=> C.P. of the first car: \(26,000 * \frac{100 }{ 130} = 20,000\)

=> C.P. of second car: 60 percent less than the C.P. of first car: \(20,000 * \frac{40 }{ 100} = 8,000\)

=> C.P. 1 = 20,000

=> S.P. 1 = 26,000

=> Profit 1 = 26,000 – 20,000 = 6,000

=> C.P. 2 = 8,000

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

=> Overall loss: 6,000 - 12,000 = -6,000

Therefore, B is the correct answer.

Answer B
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post  09 Aug 2021, 20:42
Que: If both 11 and \(7^2\) are factors of ‘\(a * 4^5 * 6^3 * 7\), then what is the smallest possible value of a?

(A) 7
(B) 11
(C) 49
(D) 77
(E) 539
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post  10 Aug 2021, 21:20
MathRevolution wrote:
Que: If both 11 and \(7^2\) are factors of ‘\(a * 4^5 * 6^3 * 7\), then what is the smallest possible value of a?

(A) 7
(B) 11
(C) 49
(D) 77
(E) 539



Solution: Express the given number \(a * 4^5 * 6^3 * 7\) in prime factors as \(a * 2^10 * 2^3 * 3^3 * 7\)

For 11 to be the factor it should be contained in it. If we remove ‘a’ then we don’t have 11. Hence a = 11.

=> 7 is contained already and hence we need 1 more 7 so that \(7^2\) is the factor and hence 7 should also be in a.

Thus, smallest value of a = 7 * 11 = 77

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  10 Aug 2021, 21:26
Que: Find the number of keystrokes required to type numbers from 100 to 1000?

(A) 2,700
(B) 2,701
(C) 2,703
(D) 2,704
(E) 3,604
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MathRevolution
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post  11 Aug 2021, 20:58
MathRevolution wrote:
Que: Find the number of keystrokes required to type numbers from 100 to 1000?

(A) 2,700
(B) 2,701
(C) 2,703
(D) 2,704
(E) 3,604



Solution: The number range is from 100 to 1000.

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

=> Four digit number = 1000 [Will need 4 key stroke] = 4 = 4 key strokes

=> Total keystrokes = 2700 + 4 = 2704

Therefore, 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  11 Aug 2021, 21:04
Que: Find the number of trailing zeroes after the rightmost non-zero digit in the value of 55!?

A) 3
B) 5
C) 7
D) 11
E) 13
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink] New post  12 Aug 2021, 20:58
MathRevolution wrote:
Que: Find the number of trailing zeroes after the rightmost non-zero digit in the value of 55!?

A) 3
B) 5
C) 7
D) 11
E) 13




Solution: 55! = 55 * 54 * 53 *………. * 3 * 2 * 1

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

=> Numbers in 55! , which has ‘5’ as the factor are: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55

=> 25 and 50 will have ‘2’ (5’s). Hence, we have 13 ‘5’s’ and at least 13 even numbers in 55! , which when multiplied by 5 will result in ‘0’.

E is the correct answer.

Answer E.
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Re: PS Expert - Math Revolution: Ask Me Anything about GMAT PS [#permalink]
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