Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 20 Jul 2019, 04:50

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 21 Oct 2013
Posts: 414
Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

### Show Tags

20 Jul 2014, 02:55
4
15
00:00

Difficulty:

75% (hard)

Question Stats:

62% (02:48) correct 38% (02:59) wrong based on 296 sessions

### HideShow timer Statistics

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)
Math Expert
Joined: 02 Sep 2009
Posts: 56303
Re: Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

### Show Tags

20 Jul 2014, 05:51
4
2
goodyear2013 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 x=y=10.

So, Henry eats 10 scones in 10% of the time it takes Rachel to eat 10 scones. This means that Henry eats 10 times as fast as Rachel.

Rachel eats 4 scones in 10 minutes --> 8 scones in 20 minutes.
Henry will take 20/10 = 2 minutes to eat 8 scones.

Plug y = 10 into the options to see which one of them gives 2. Only A fits.

_________________
##### General Discussion
Intern
Joined: 14 Feb 2013
Posts: 19
Re: Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

### Show Tags

20 Jul 2014, 20:30
goodyear2013 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 Henry eats 50 cones in 50% of time it takes Rachel to eat 100 cones.

Then, X = 50 , Y = 100

Rachel eats 4 cones in 10 minutes

=

Rachel eats 1 cone in 5/2 minutes
Rachel eats 100 cones in 250 minutes

Since Henry eats 50 cones in 50% of time it takes Rachel to eat 100 cones = 250/2 = 125 minutes

Henry eats 50 cones in 125 minutes
Henry eats 8 cones in 20 minutes

Both options A & D give the answer 20 when values are plugged in

Is the question right, or should we change our plugged values if such a situation arises?
Intern
Joined: 14 Feb 2013
Posts: 19
Re: Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

### Show Tags

20 Jul 2014, 20:35
Bunuel wrote:
goodyear2013 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 x=y=10.

So, Henry eats 10 scones in 10% of the time it takes Rachel to eat 10 scones. This means that Henry eats 10 times as fast as Rachel.

Rachel eats 4 scones in 10 minutes --> 8 scones in 20 minutes.
Henry will take 20/10 = 2 minutes to eat 8 scones.

Plug y = 10 into the options to see which one of them gives 2. Only A fits.

If Henry eats 50 cones in 50% of time it takes Rachel to eat 100 cones.

Then, X = 50 , Y = 100

Rachel eats 4 cones in 10 minutes

=

Rachel eats 1 cone in 5/2 minutes
Rachel eats 100 cones in 250 minutes

Since Henry eats 50 cones in 50% of time it takes Rachel to eat 100 cones = 250/2 = 125 minutes

Henry eats 50 cones in 125 minutes
Henry eats 8 cones in 20 minutes

Both options A & D give the answer 20 when values are plugged in

I plugged in other values as well, same case.

Something wrong with the question?
Math Expert
Joined: 02 Sep 2009
Posts: 56303
Re: Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

### Show Tags

21 Jul 2014, 11:59
hamzakb wrote:
goodyear2013 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 Henry eats 50 cones in 50% of time it takes Rachel to eat 100 cones.

Then, X = 50 , Y = 100

Rachel eats 4 cones in 10 minutes

=

Rachel eats 1 cone in 5/2 minutes
Rachel eats 100 cones in 250 minutes

Since Henry eats 50 cones in 50% of time it takes Rachel to eat 100 cones = 250/2 = 125 minutes

Henry eats 50 cones in 125 minutes
Henry eats 8 cones in 20 minutes

Both options A & D give the answer 20 when values are plugged in

Is the question right, or should we change our plugged values if such a situation arises?

For plug-in method it might happen that for some particular number(s) more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only.
_________________
Intern
Joined: 07 Feb 2015
Posts: 45
Re: Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

### Show Tags

14 Mar 2015, 01:55
4
Rate at which rachel eats = 4/10 spm(scones per minute)=0.4spm
Time taken to eat y scones=T=y/0/.4=2.5y

according to the statement,
rate at which henry eats scones=x/((x/100)T)=100/2.5y=40/y spm
time taken to eat 8 scones= 8/(40/y)=y/5

(A)
_________________
Kudos if it helped you in any way
VP
Joined: 07 Dec 2014
Posts: 1207
Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

### Show Tags

Updated on: 28 Nov 2015, 13:29
rachel eats Y scones in 5Y/2 minutes
henry eats X scones in (X/100)(5Y/2)=XY/40 minutes
henry's rate=X/(XY/40)=40/Y scones per minute
henry's time for eating 8 scones=8/(40/Y)=Y/5 minutes

Originally posted by gracie on 14 Nov 2015, 22:29.
Last edited by gracie on 28 Nov 2015, 13:29, edited 1 time in total.
Math Expert
Joined: 02 Aug 2009
Posts: 7764
Re: Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

### Show Tags

14 Nov 2015, 23:12
goodyear2013 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)

Hi,
R eats Y scones ,say in Z minutes..
so R will eat 4 cones in 4Z/Y
but this is equal to 10 min
so 4z/y=10 or Z=5Y/2
thus R will eat 8 in 5Y..

now lets see H..
H eats X scones in X% of time R takes, which is 5Y/2 or X scones in X/100*5Y/2=XY/40..
so H eats 8 scones in 8*XY/40(X)=Y/5
ans A
_________________
Senior Manager
Joined: 03 Apr 2013
Posts: 273
Location: India
Concentration: Marketing, Finance
GMAT 1: 740 Q50 V41
GPA: 3
Re: Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

### Show Tags

07 May 2017, 05:13
chetan2u wrote:
goodyear2013 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)

Hi,
R eats Y scones ,say in Z minutes..
so R will eat 4 cones in 4Z/Y
but this is equal to 10 min
so 4z/y=10 or Z=5Y/2
thus R will eat 8 in 5Y..

now lets see H..
H eats X scones in X% of time R takes, which is 5Y/2 or X scones in X/100*5Y/2=XY/40..
so H eats 8 scones in 8*XY/40(X)=Y/5
ans A

Hi chetan2u

Is there a problem with the wording? I didn't get a clue how the answers have come, because the wording is kind of weird for me.
_________________
Spread some love..Like = +1 Kudos
Math Expert
Joined: 02 Aug 2009
Posts: 7764
Re: Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

### Show Tags

07 May 2017, 06:39
ShashankDave wrote:
chetan2u wrote:
goodyear2013 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)

Hi,
R eats Y scones ,say in Z minutes..
so R will eat 4 cones in 4Z/Y
but this is equal to 10 min
so 4z/y=10 or Z=5Y/2
thus R will eat 8 in 5Y..

now lets see H..
H eats X scones in X% of time R takes, which is 5Y/2 or X scones in X/100*5Y/2=XY/40..
so H eats 8 scones in 8*XY/40(X)=Y/5
ans A

Hi chetan2u

Is there a problem with the wording? I didn't get a clue how the answers have come, because the wording is kind of weird for me.

Hi,

The wording is fine but complicated which would be very rare in actuals.

You can actually combine first two sentences to get,
Henry eats x scones in x%of 10 minutes in which Rachel eats 4 scones. In how much time will Henry eat 8 scones.

And if you combine further and want to remove x too..
Henry eats 1 scones in 1% of 10 minutes in which Rachel eats 4 scones. In how much time will Henry eat 8 scones.

Henry will eat 8 in 8% of 10 minutes, so $$\frac{8}{100}*10=\frac{8}{10}$$ or 4/5 minutes...

Now y here is 4, substitute and straight A is the answer..
_________________
Intern
Joined: 16 Apr 2015
Posts: 7
Re: Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

### Show Tags

09 May 2017, 10:12
1
This is a fairly simple problem if one views in terms of unitary method.
Rachel: 4 cones in 10 mins
1 cone in 10/4 mins
Y cones in (10/4)Y mins

Henery: Eats X cones in X% of (Time taken by Rachel to eat Y cones)
Eats 8 cones in 8% of ((10*Y)/4) = Y/5
OA: A
Manager
Joined: 14 Oct 2015
Posts: 246
GPA: 3.57
Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

### Show Tags

Updated on: 15 Jan 2018, 23:23
goodyear2013 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)

We know that
$$Rate * Time = Work$$ --- 1
Consequently $$Time = \frac{Work}{Rate}$$ -- 2
and $$Rate = \frac{Work}{Time}$$ -- 3

For Rachel
$$Work = Y$$
$$Time = T$$
$$Rate = \frac{Y}{T} = \frac{4}{10} = 0.4$$

so Time T for Rachel becomes, $$\frac{Y}{0.4}$$ .. using -- 2

For Henry,
$$Time = \frac{T*X}{100}$$
$$Work = X$$
$$Rate = \frac{Work}{Time} = \frac{X}{T*X/100} = 100/T$$

Now using -- 2

$$Time = \frac{X}{100/T} = \frac{TX}{100}$$

Replacing Rachel's Time of $$\frac{Y}{0.4}$$ and Henry's 8 scones as $$X$$, we get.

$$Time = \frac{Y*8}{100*0.4} = \frac{8Y}{40} = \frac{Y}{5}$$
_________________
Please hit Kudos if this post helped you inch closer to your GMAT goal.
Procrastination is the termite constantly trying to eat your GMAT tree from the inside.
There is one fix to every problem, working harder!

Originally posted by jedit on 15 Jan 2018, 20:12.
Last edited by jedit on 15 Jan 2018, 23:23, edited 1 time in total.
Intern
Joined: 31 Dec 2017
Posts: 28
Concentration: Finance
Re: Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

### Show Tags

15 Jan 2018, 23:22
Rachel eats 4 scones in 10 mins, so time taken to eat a scone = 10/4 mins.

Time taken by Rachel to eat Y scones = 10Y/4 mins.

Time taken by Henry to eat 8 scones = 8%(10Y/4) mins = 80Y/400 = Y/5 mins. Ans - A.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6968
Location: United States (CA)
Re: Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

### Show Tags

18 Jan 2018, 14:26
goodyear2013 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)

The rate of Rachel is 4/10 = 2/5.

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 minutes. If we let m = the number of minutes Henry eats 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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

CEO
Joined: 12 Sep 2015
Posts: 3852
Re: Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

### Show Tags

15 Jan 2019, 11:20
Top Contributor
goodyear2013 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

Cheers,
Brent

RELATED VIDEO FROM OUR COURSE

_________________
Test confidently with gmatprepnow.com
Re: Henry eats X scones in X percent of the time it takes Rachel   [#permalink] 15 Jan 2019, 11:20
Display posts from previous: Sort by