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

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

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20 Jul 2014, 01:55
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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)
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 43862
Re: Henry eats X scones in X percent of the time it takes Rachel [#permalink]

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20 Jul 2014, 04:51
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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.

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Re: Henry eats X scones in X percent of the time it takes Rachel [#permalink]

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20 Jul 2014, 19:30
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?
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Joined: 14 Feb 2013
Posts: 20
Re: Henry eats X scones in X percent of the time it takes Rachel [#permalink]

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20 Jul 2014, 19:35
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: 43862
Re: Henry eats X scones in X percent of the time it takes Rachel [#permalink]

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21 Jul 2014, 10:59
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.
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Re: Henry eats X scones in X percent of the time it takes Rachel [#permalink]

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14 Mar 2015, 00:55
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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)
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Posts: 906
Henry eats X scones in X percent of the time it takes Rachel [#permalink]

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14 Nov 2015, 21:29
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

Last edited by gracie on 28 Nov 2015, 12:29, edited 1 time in total.
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Posts: 5660
Re: Henry eats X scones in X percent of the time it takes Rachel [#permalink]

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14 Nov 2015, 22:12
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
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Re: Henry eats X scones in X percent of the time it takes Rachel [#permalink]

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07 May 2017, 04:13
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.
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Re: Henry eats X scones in X percent of the time it takes Rachel [#permalink]

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07 May 2017, 05:39
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..
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: Henry eats X scones in X percent of the time it takes Rachel [#permalink]

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09 May 2017, 09:12
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
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Henry eats X scones in X percent of the time it takes Rachel [#permalink]

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15 Jan 2018, 19:12
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)

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.

$$Time = \frac{Y*8}{100*0.4} = \frac{8Y}{40} = \frac{Y}{5}$$
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Last edited by jedit on 15 Jan 2018, 22:23, edited 1 time in total.
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Re: Henry eats X scones in X percent of the time it takes Rachel [#permalink]

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15 Jan 2018, 22:22
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.
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Re: Henry eats X scones in X percent of the time it takes Rachel [#permalink]

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18 Jan 2018, 13:26
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.

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Re: Henry eats X scones in X percent of the time it takes Rachel   [#permalink] 18 Jan 2018, 13:26
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