GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Oct 2018, 03:51

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Senior Manager
Senior Manager
User avatar
Joined: 21 Oct 2013
Posts: 420
Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

Show Tags

New post 20 Jul 2014, 02:55
4
13
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

63% (02:51) correct 37% (03:00) wrong based on 257 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)
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50004
Re: Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

Show Tags

New post 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.

Answer: A.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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

Show Tags

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

Show Tags

New post 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.

Answer: A.


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
User avatar
V
Joined: 02 Sep 2009
Posts: 50004
Re: Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

Show Tags

New post 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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 07 Feb 2015
Posts: 46
Re: Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

Show Tags

New post 14 Mar 2015, 01:55
3
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
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1104
Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

Show Tags

New post 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
User avatar
V
Joined: 02 Aug 2009
Posts: 6961
Re: Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

Show Tags

New post 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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Senior Manager
Senior Manager
User avatar
G
Joined: 03 Apr 2013
Posts: 280
Location: India
Concentration: Marketing, Finance
GMAT 1: 740 Q50 V41
GPA: 3
GMAT ToolKit User
Re: Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

Show Tags

New post 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
User avatar
V
Joined: 02 Aug 2009
Posts: 6961
Re: Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

Show Tags

New post 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.

Now answer is straight ...
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..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Intern
Intern
User avatar
B
Joined: 16 Apr 2015
Posts: 8
Re: Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

Show Tags

New post 09 May 2017, 10:12
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
Senior Manager
Senior Manager
avatar
P
Joined: 14 Oct 2015
Posts: 250
GPA: 3.57
Reviews Badge
Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

Show Tags

New post 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
Intern
User avatar
B
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

New post 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
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3896
Location: United States (CA)
Re: Henry eats X scones in X percent of the time it takes Rachel  [#permalink]

Show Tags

New post 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.

Answer: A
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

GMAT Club Bot
Re: Henry eats X scones in X percent of the time it takes Rachel &nbs [#permalink] 18 Jan 2018, 14:26
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.