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05 Nov 2011, 13:23
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
69% (02:16) correct
31%
(02:32)
wrong
based on 2591
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Machine A can complete a certain job in x hours. Machine B can complete the same job in y hours. If A and B work together at their respective rates to complete the job, which of the following represents the fraction of the job that B will not have to complete because of A's help?
A) (x – y)/(x + y)
B) x/(y – x)
C) (x + y)/(xy)
D) y/(x – y)
E) y/(x + y)
A) (x – y)/(x + y)
B) x/(y – x)
C) (x + y)/(xy)
D) y/(x – y)
E) y/(x + y)
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27 Jan 2012, 17:20
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docabuzar
Machine A can complete a certain job in x hours. Machine B can complete the same job in y hours. If A and B work together at their respective rates to complete the job, which of the following represents the fraction of the job that B will not have to complete because of A's help?
A. (x – y)/(x + y)
B. x/(y–x)
C. (x+y)/xy
D. y/(x-y)
E. y/(x+y)
A. (x – y)/(x + y)
B. x/(y–x)
C. (x+y)/xy
D. y/(x-y)
E. y/(x+y)
Working together A and B complete the job in \(\frac{xy}{x+y}\) hours (as time is a reciprocal of rate then take the reciprocal of combined rate, which is \(\frac{1}{x}+\frac{1}{y}=\frac{x+y}{xy}\));
Now, in \(\frac{xy}{x+y}\) hours A will complete \(\frac{1}{x}*\frac{xy}{x+y}=\frac{y}{x+y}\) part of the job (rate*time=job) and this will be the part which B will not have to complete.
Answer: E.
sudish
Joined: 09 Sep 2011
Last visit: 15 Nov 2014
Posts: 120
Given Kudos: 16
Status:Enjoying the MBA journey :)
Location: United States (DC)
Concentration: General Management, Entrepreneurship
Schools: CBS '15 (D) Ross '15 (D) Anderson '15 (D) Johnson '15 (WL) ISB '14 (D) Kellogg '15 (D) Olin '15 (WA$) McDonough '15 (M)
GMAT 1: 710 Q49 V38
WE:Corporate Finance (Other)
Schools: CBS '15 (D) Ross '15 (D) Anderson '15 (D) Johnson '15 (WL) ISB '14 (D) Kellogg '15 (D) Olin '15 (WA$) McDonough '15 (M)
GMAT 1: 710 Q49 V38
Posts: 120
05 Nov 2011, 14:31
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Since Machine A can complete the job in 'x' hours, the job completed by Machine A in 1 hour will be 1/x
Similarly, since Machine B completes the job in 'y' hours, Machine B will complete 1/y of the job in 1 hour
Hence the job completed in 1 hour when A and B work together at their respective rates is:
1/x + 1/y = (x+y)/xy
Since A completes 1/x of this job, 1/x of the total job is what Machine B will not have to complete because of Machine A's help.
So, the required quantity is (1/x) of (x+y)/xy i.e. (1/x)/(x+y)/xy = xy/x(x+y) = y/(x+y)
Hence, in my opinion, the answer should be option E.
Similarly, since Machine B completes the job in 'y' hours, Machine B will complete 1/y of the job in 1 hour
Hence the job completed in 1 hour when A and B work together at their respective rates is:
1/x + 1/y = (x+y)/xy
Since A completes 1/x of this job, 1/x of the total job is what Machine B will not have to complete because of Machine A's help.
So, the required quantity is (1/x) of (x+y)/xy i.e. (1/x)/(x+y)/xy = xy/x(x+y) = y/(x+y)
Hence, in my opinion, the answer should be option E.
