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

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Director
Joined: 07 Jun 2004
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Machine X takes 20 hours longer than machine Y to produce 10 [#permalink]  02 Mar 2011, 14:23
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67% (03:14) correct 32% (02:22) wrong based on 78 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

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Director
Status: Matriculating
Affiliations: Chicago Booth Class of 2015
Joined: 03 Feb 2011
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Re: Word problem [#permalink]  02 Mar 2011, 15:02
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: 934
Followers: 11

Kudos [?]: 163 [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: 4032
Location: Pune, India
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Kudos [?]: 3616 [4] , given: 144

Re: Word problem [#permalink]  03 Mar 2011, 18:22
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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

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

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews SVP Joined: 16 Nov 2010 Posts: 1698 Location: United States (IN) Concentration: Strategy, Technology Followers: 28 Kudos [?]: 261 [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) Senior Manager Joined: 08 Nov 2010 Posts: 424 WE 1: Business Development Followers: 6 Kudos [?]: 28 [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: 4032 Location: Pune, India Followers: 859 Kudos [?]: 3616 [0], given: 144 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 Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
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Intern
Joined: 27 Feb 2011
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Kudos [?]: 0 [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: 465
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 14

Kudos [?]: 148 [1] , given: 11

Re: Word problem [#permalink]  03 Dec 2012, 01:25
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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.
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VP
Joined: 06 Sep 2013
Posts: 1179
Location: United States
Concentration: Finance, General Management
Schools: Stanford '17
GPA: 3.5
WE: Corporate Finance (Investment Banking)
Followers: 6

Kudos [?]: 73 [0], given: 125

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
Re: Machine X takes 20 hours longer than machine Y to produce 10   [#permalink] 12 Feb 2014, 12:52
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