Henry eats X scones in X percent of the time it takes Rachel

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

Henry eats X scones in X percent of the time it takes Rachel

by swerve » Tue Jan 15, 2019 9:19 am

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Henry eats X scones in X percent of the time it takes Rachel to eat Y scones. If Rachel eats four scones in ten minutes, then the number of minutes it takes Henry to eat 8 scones must be equal to which of the following?

A. Y/5
B. 320/Y
C. 100Y/(5X)
D. XY/250
E. Y/(5X)

The OA is A

Source: Economist GMAT

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Source: Beat The GMAT — Problem Solving | Tue Jan 15, 2019 9:19 am

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by Brent@GMATPrepNow » Tue Jan 15, 2019 10:08 am

swerve wrote:Henry eats X scones in X percent of the time it takes Rachel to eat Y scones. If Rachel eats four scones in ten minutes, then the number of minutes it takes Henry to eat 8 scones must be equal to which of the following?

A. Y/5
B. 320/Y
C. 100Y/(5X)
D. XY/250
E. Y/(5X)

Let's use the INPUT-OUTPUT approach.
Let's assign some values of X and Y so that they satisfy the information in the question.

Let X = 25. This means Henry eats 25 scones in 25 percent of the time it takes Rachel to eat Y scones
Let Y = 100. This means Henry eats 25 scones in 25 percent of the time it takes Rachel to eat 100 scones
Notice that this implies Rachel and Henry eat at the SAME RATE.
Here's why: If Henry eats 25 scones in 1/4 the time it takes Rachel to eat 100 scones, then if we quadruple Henry's eating time, then he will eat 100 scones in the SAME TIME it take Rachel to each 100 score.

If Rachel eats four scones in ten minutes, then the number of minutes it takes Henry to eat 8 scones must be equal to which of the following?
Henry is going to eat TWICE as many scones as Rachel.
Since Henry and Rachel eat at the SAME RATE, the time it takes Henry to eat 8 scones will be TWICE the time it takes Rachel to each 4 scones.
So it will take Henry 20 minutes to eat 8 scones

So, when X = 25 and Y = 100, the answer to the question (aka the OUTPUT) will be 20

Now check the answer choices to see which one yields an OUTPUT of 20 when we INPUT X = 25 and Y = 100
A. Y/5 = 100/5 = 20. Perfect! KEEP A
B. 320/Y = 320/100 = 3.2. No good. We want an output of 20
C. 100Y/(5X) = (100)(100)/(5)(25) = 80. No good. We want an output of 20
D. XY/250 = (100)(25)/250 = 10. No good. We want an output of 20
E. Y/(5X) = (100)/(5)(25) = 0.8. No good. We want an output of 20

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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by GMATGuruNY » Tue Jan 15, 2019 10:28 am

swerve wrote:. If Rachel eats four scones in ten minutes, then the number of minutes it takes Henry to eat 8 scones must be equal to which of the following?

A. Y/5
B. 320/Y
C. 100Y/(5X)
D. XY/250
E. Y/(5X)

Let X=8 and Y=4.

Henry eats X scones in X percent of the time it takes Rachel to eat Y scones.
Since Henry eats X=8 scones in 8% of the time it takes Rachel to eat Y=4 scones -- 10 minutes, according to the prompt -- the time for Henry to eat 8 scones = 8% of 10 minutes = (8/100)(10) = 4/5 minute.

The number of minutes it takes Henry to eat 8 scones must be equal to which of the following?
The correct answer must yield 4/5 when X=8 and Y=4.
Only A works:
Y/5 = 4/5.

The correct answer is A.

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by Scott@TargetTestPrep » Thu Jan 17, 2019 5:53 pm

swerve wrote:Henry eats X scones in X percent of the time it takes Rachel to eat Y scones. If Rachel eats four scones in ten minutes, then the number of minutes it takes Henry to eat 8 scones must be equal to which of the following?

A. Y/5
B. 320/Y
C. 100Y/(5X)
D. XY/250
E. Y/(5X)

If we let X = 10 and Y = 4, we see that Henry eats 10 scones in 10% of the time it takes Rachel to eat 4 scones. Since Rachel eats 4 scones in 10 minutes and 10% of 10 minutes is 1 minute, that means Henry eats 10 scones in 1 minute. If we let m = the number of minutes it takes Henry to eat 8 scones, we set up the proportion:

10/1 = 8/m

10m = 8

m = 8/10 = 4/5

Thus, Henry eats 8 scones in 4/5 of a minute. However, since Y = 4, Henry eats 8 scones in Y/5 minutes.

Alternate Solution:

Let t denote the number of minutes it takes Rachel to eat Y scones. Then, it takes Henry X percent of t, or (t*X)/100 minutes to eat X scones.

If it takes Rachel t minutes to eat Y scones and 10 minutes to eat 4 scones, then we must have:

10/4 = Y/t

t = 10Y/4 = 5Y/2

Thus, it takes Henry (t*X)/100 = (5YX)/200 = XY/40 minutes to eat X scones. To find the number of minutes it takes Henry to eat 8 scones, let's denote it by s and set up another proportion:

8/s = (XY/40)/X

8/s = Y/40

s = Y/5

Answer: A

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