Combined rate, difficult without plugging values?

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Mormuse: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Thu Mar 07, 2013 5:30 am

by Mormuse » Mon Apr 08, 2013 1:39 am

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?

x - y/x + y

x/y - x

x + y/xy

y/x - y

y/x + y

Answer e

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Source: Beat The GMAT — Problem Solving | Mon Apr 08, 2013 1:39 am

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Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members; Location: Delhi, India; Thanked: 344 times

by Anju@Gurome » Mon Apr 08, 2013 1:41 am

claudayst wrote: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?

Fraction of the job that B will not have to complete = Fraction of the job that A will complete

Algebraic Approach:
In 1 hour, A completes 1/x of the job.
In 1 hour, B completes 1/y of the job.
In 1 hour, A and B together complete (1/x + 1/y) = (x + y)/xy of the job.

Hence, A and B together will complete the job in xy/(x + y) hours.
In xy/(x + y) hours A will do [xy/(x + y)]*(1/x) = y/(x + y) of the job.

The correct answer is E.

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Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members; Location: Delhi, India; Thanked: 344 times

by Anju@Gurome » Mon Apr 08, 2013 1:42 am

Tricky Approach:
Let us assume that A completes the job in zero hours, i.e. A completes the job alone and we don't need B to do any part of the job. (This is practically impossible but mathematics should hold for this situation also)

Hence, x = 0
We will put this value of x in the given options to see which of them is equal to 1.

A. (x - y)/(x + y) = -y/y = -1 --> NO
B. x/(x + y) = 0 --> NO
C. (x + y)/(xy) = Not definite --> NO
D. y/(x - y) = -y/y = -1 --> NO
E. y/(x + y) = y/y = 1 --> YES

The correct answer is E.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Apr 08, 2013 2:47 am

claudayst wrote: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?

(x - y)/(x + y)

x/(y - x)

(x + y)/xy

y/(x - y)

y/(x + y)

In other words:
What fraction of the job will be completed by A?

The TIME RATIO for A and B = x:y.
Since time and rate are reciprocals, the RATE RATIO for A and B = y : x.
Implication of the rate ratio:
Of every y+x units produced each hour, A produces y units and B produces x units.
Thus, (work produced by A each hour)/(total work produced each hour) = y/(y+x).

The correct answer is E.

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