Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 28 Apr 2015, 05:12

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Machine X takes 20 hours longer than machine Y to produce 10

 Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Director
Joined: 07 Jun 2004
Posts: 614
Location: PA
Followers: 3

Kudos [?]: 270 [3] , given: 22

Machine X takes 20 hours longer than machine Y to produce 10 [#permalink]  02 Mar 2011, 14:23
3
This post received
KUDOS
7
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

68% (03:29) correct 32% (02:27) wrong based on 141 sessions
Machine X takes 20 hours longer than machine Y to produce 1080 Widgets. Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. How many widgets per hour does machine X produce

A. 100
B. 65
C. 25
D. 11
E. 9
[Reveal] Spoiler: OA

_________________

If the Q jogged your mind do Kudos me : )

Director
Status: Matriculating
Affiliations: Chicago Booth Class of 2015
Joined: 03 Feb 2011
Posts: 926
Followers: 13

Kudos [?]: 218 [0], given: 123

Re: Word problem [#permalink]  02 Mar 2011, 15:02
1
This post was
BOOKMARKED
Machine X rate : x wid / hr
Machine Y rate : y wid / hr
Given y = 1.2 x --------(1)

1080 / x - 1080 / y = 20 ----(2)
1) + 2)
Solving get x = 9 wid / hr

rxs0005 wrote:
Machine X takes 20 hours longer than machine Y to produce 1080 Widgets.
Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. How many widgets per hour does machine X produce

100

65

25

11

9
Director
Status: Matriculating
Affiliations: Chicago Booth Class of 2015
Joined: 03 Feb 2011
Posts: 926
Followers: 13

Kudos [?]: 218 [0], given: 123

Re: Word problem [#permalink]  02 Mar 2011, 15:05
Back solving -
Equation (2) reduces to 54/x - 54/y = 1. Hence x should be a factor of 54. E it is.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 5437
Location: Pune, India
Followers: 1325

Kudos [?]: 6724 [4] , given: 176

Re: Word problem [#permalink]  03 Mar 2011, 18:22
4
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
rxs0005 wrote:
Machine X takes 20 hours longer than machine Y to produce 1080 Widgets.
Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. How many widgets per hour does machine X produce

100

65

25

11

9

Another approach:Use Ratios

Machine Y produces 20% more widgets so its speed is 6/5 of X.
Speed of X: Speed of Y = 5:6
Time taken by X: Time taken by Y = 6:5 (if amount of work is kept constant, time will be inversely proportional to speed)
This difference of 1 in their time accounts for 20 hrs.
Hence X takes 6*20 = 120 hrs to produce 1080 widgets. In 1 hour, it produces 1080/120 = 9 widgets.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Veritas Prep GMAT course is coming to India. Enroll in our weeklong Immersion Course that starts March 29!

Veritas Prep Reviews

SVP
Joined: 16 Nov 2010
Posts: 1687
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 31

Kudos [?]: 340 [2] , given: 36

Re: Word problem [#permalink]  03 Mar 2011, 21:37
2
This post received
KUDOS
My take :

Machine Y -> Y hrs to produce 1080 Widgets, So Machine X -> Y + 20 to produce 1080 Widgets

Y -> 1080/Y Widgets X -> 1080/(Y+20)

1/Y = 1.2 * 1/(y+20)

5y + 100 = 6y => y = 100, so Machine X - 120 hrs to 1080

hence Machine X -> 1080/120 = 9
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Senior Manager
Joined: 08 Nov 2010
Posts: 422
WE 1: Business Development
Followers: 7

Kudos [?]: 46 [0], given: 161

Re: Word problem [#permalink]  05 Mar 2011, 09:26
Karishma, can u explain ur system in more details plz?
y produces 20% faster so as far as i understand
if x produces 5
Y produces 6/5
in one hour.

hmm - im stuck. ill be happy to learn ur way - ur ways are amazing. thanks.+1
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 5437
Location: Pune, India
Followers: 1325

Kudos [?]: 6724 [0], given: 176

Re: Word problem [#permalink]  05 Mar 2011, 19:45
Expert's post
144144 wrote:
Karishma, can u explain ur system in more details plz?
y produces 20% faster so as far as i understand
if x produces 5
Y produces 6/5
in one hour.

hmm - im stuck. ill be happy to learn ur way - ur ways are amazing. thanks.+1

What I use a lot is ratios. Ratios eliminate the need for equations.

In different questions, you will need to handle data differently to get a ratio.
e.g.
1.
Speed of x is 40 m/hr and speed of y is 60 m/hr.
Then ratio of speeds is 40:60 i.e. 2:3 (lowest representation - in ratios 2:3 is same as 4:6 which is same as 20:30 etc)

2.
Speed of x is 20% more than that of y.
If speed of y is 1, speed of x is 6/5 (i.e. 20% = 1/5 more than 1). Ratio of speed of X:Y = 6/5:1 or 6:5 (Multiplying the ratio by 5) or simply, since speed of x is more, x will be 6 and y will be 5.

Now, quantities such as time, rate and work done are related to each other.

We know W = R*T

If two machines A and B with rates of work in the ratio 6:5 work for 1 hr each, who will do more work?
Since they are both working for the same time, A will do more work since its rate is higher. How much more work will A do as compared to B? Since A's rate is 20% higher, A will do 20% more work...
Now, let me ask you this - if both A and B do the same amount of work, who will take less time?
Since A's rate is 20% more, A will take less time. How much less time will it take? Let's say there was 30 units of work that each did.
A's rate - 6 units/hr, time taken - 30/6 = 5 hrs
B's rate - 5 units/hr, time taken - 30/5 = 6 hrs

So basically time taken flips the speed (time is inversely proportional to speed)
Time taken by A:B = 5:6

Now think, I tell you that A takes 10 hrs to do a job. How long will B take to do the same job? 12 hrs because they take time in the ratio 5:6.
Now, if I tell you that for a particular work, difference between time taken by A and time taken by B is 10 hrs. How long did A take to finish the job?
Since the difference between the times should be 10, they must have taken 50 and 60 hrs to do the work.

These are a few concepts that we use to solve questions using ratios. The next topic I am taking up on my Veritas blog is ratios. Watch out for the first post early next week... It should make these concepts clearer...
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Veritas Prep GMAT course is coming to India. Enroll in our weeklong Immersion Course that starts March 29!

Veritas Prep Reviews

Intern
Joined: 27 Feb 2011
Posts: 48
Followers: 0

Kudos [?]: 3 [0], given: 9

Re: Word problem [#permalink]  05 Mar 2011, 23:45
VeritasPrepKarishma wrote:
Another approach:Use Ratios

Machine Y produces 20% more widgets so its speed is 6/5 of X.
Speed of X: Speed of Y = 5:6
Time taken by X: Time taken by Y = 6:5 (if amount of work is kept constant, time will be inversely proportional to speed)
This difference of 1 in their time accounts for 20 hrs.
Hence X takes 6*20 = 120 hrs to produce 1080 widgets. In 1 hour, it produces 1080/120 = 9 widgets.

innovative
Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 17

Kudos [?]: 256 [1] , given: 11

Re: Word problem [#permalink]  03 Dec 2012, 01:25
1
This post received
KUDOS
Rate of X = $$\frac{1080}{y+20}=w$$
Rate of Y = $$\frac{1080}{y}=1.2w$$

Combine:
$$\frac{1080}{y+20}(1.2) = \frac{1080}{y}$$
$$y+20=1.2y==>.2y=20==>y=100$$

$$\frac{1080}{100+20}=\frac{1080}{120}=9$$

9 widgets in 1 hour.
_________________

Impossible is nothing to God.

SVP
Joined: 06 Sep 2013
Posts: 2030
Concentration: Finance
GMAT 1: 710 Q48 V39
Followers: 24

Kudos [?]: 292 [0], given: 354

Re: Machine X takes 20 hours longer than machine Y to produce 10 [#permalink]  12 Feb 2014, 12:52
Here's a short and elegant way to solve

1/x - 1/y = 20 / 1080 = 1/54

y = 1.2x

1/x - 1/1.2x = 1/54

1/6x = 54

x = 9

E is the answer.

But let me tell you that I really liked Karishma's approach using ratios too.

Cheers
J
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 4700
Followers: 291

Kudos [?]: 52 [0], given: 0

Re: Machine X takes 20 hours longer than machine Y to produce 10 [#permalink]  30 Mar 2015, 09:42
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Optimus Prep Instructor
Joined: 06 Nov 2014
Posts: 126
Followers: 0

Kudos [?]: 27 [0], given: 0

Re: Machine X takes 20 hours longer than machine Y to produce 10 [#permalink]  31 Mar 2015, 02:25
Expert's post
rxs0005 wrote:
Machine X takes 20 hours longer than machine Y to produce 1080 Widgets. Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. How many widgets per hour does machine X produce

A. 100
B. 65
C. 25
D. 11
E. 9

Machine Y produces 20 percent more widgets in an hour than machine x does in an hour.
So if machine X produces 100 widgets, then machine Y produces 120 widgets.
Ratio of 120/100 = 6/5.
This is their speed of work (Y:X).
i.e. speed of their work (X:Y) = 5/6

Now, time is inversely proportional to speed.
Hence the ratio of the time spent (X:Y)= 6/5
Let us assume that they spend 6x and 5x hours.
Given that 6x-5x = 20
So, x = 20.
Hence 6x = 6*20 = 120 hours.
Hence X takes 120 hours to produce 1080 widgets.
So, in 1 hour, it can produce (1 * 1080)/120
= 9

Hence option (E).
--
Optimus Prep's GMAT On Demand course for only \$299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: http://www.optimus-prep.com/gmat-on-demand-course
_________________

Best regards,

Jesse I GMAT Tutor at Optimus Prep I gmat@optimus-prep.com

Website: http://www.optimus-prep.com/gmat

Best Posts:

How To Choose The Best GMAT Course Option On GMATCLUB:

http://gmatclub.com/forum/how-to-choose-the-best-gmat-course-option-on-gmatclub-195579.html

Ultimate GMAT On Demand Course Comparison:

http://gmatclub.com/forum/ultimate-gmat-on-demand-course-comparison-compare-take-the-best-195568.html

Ultimate Study Plan For New GMAT Test Takers:

http://gmatclub.com/forum/ultimate-study-plan-for-new-gmat-test-takers-by-optimus-prep-195524.html

Ultimate GMAT Re-Tkaing Guide:

http://gmatclub.com/forum/ultimate-gmat-re-taking-guide-by-optimus-prep-guaranteed-results-193972.html

Ultimate GMAT Online Private Tutoring Comparison:

http://gmatclub.com/forum/ultimate-gmat-online-private-tutoring-comparison-compare-select-195569.html

Ultimate GMAT Private Tutoring Comparison:

http://gmatclub.com/forum/ultimate-gmat-private-tutoring-comparison-compare-select-the-best-195577.html

Ultimate GMAT Online Class Course Comparison:

http://gmatclub.com/forum/ultimate-gmat-online-class-course-comparison-compare-select-195578.html

Intern
Joined: 02 Jan 2015
Posts: 4
Followers: 0

Kudos [?]: 3 [0], given: 2

Re: Machine X takes 20 hours longer than machine Y to produce 10 [#permalink]  04 Apr 2015, 05:18
rxs0005 wrote:
Machine X takes 20 hours longer than machine Y to produce 1080 Widgets. Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. How many widgets per hour does machine X produce

A. 100
B. 65
C. 25
D. 11
E. 9

I think the fastest way to solve such problem is to do POE:
Find out the factors of 1080 = 2x2x2x3x3x3x3x3x5

To get the per hour rate for each machine, it has to be a factor of 1080. In the answer choices, we can see only 9 satisfies the criteria.
Director
Joined: 07 Aug 2011
Posts: 535
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
Followers: 1

Kudos [?]: 133 [0], given: 71

Machine X takes 20 hours longer than machine Y to produce 10 [#permalink]  04 Apr 2015, 05:52
rxs0005 wrote:
Machine X takes 20 hours longer than machine Y to produce 1080 Widgets. Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. How many widgets per hour does machine X produce

A. 100
B. 65
C. 25
D. 11
E. 9

machine X takes 20 hrs more to produce 1080 widgets
OR
machine X takes 1 hr more to produce 54 widgets

54/X - 1 =54/1.2X

54/X - 54/1.2X = 1

now we can solve this quadratic equation , but we do not need to . 54 is divisible only by 9 in the answer options, so lets substitute X=9
6 - 5 = 1 .

Clearly X=9 is the answer.
_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the to appreciate my post !!

Machine X takes 20 hours longer than machine Y to produce 10   [#permalink] 04 Apr 2015, 05:52
Similar topics Replies Last post
Similar
Topics:
14 It takes machine A 'x' hours to manufacture a deck of cards 10 10 Jun 2010, 05:23
It takes machine A x hours to manufacture a deck of cards 2 26 Aug 2007, 19:30
It takes machine A x hours to manufacture a deck of cards 2 09 Nov 2006, 20:47
It takes machine A x hours to manufacture a deck of cards 2 28 Sep 2006, 16:19
It takes machine A x hours to manufacture a deck of cards 3 05 Feb 2006, 20:53
Display posts from previous: Sort by

# Machine X takes 20 hours longer than machine Y to produce 10

 Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO 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®.