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by tapanmittal » Tue Aug 25, 2015 7:15 pm
Machine A currently takes x hours to complete a certain job. Machine B currently takes y hours to
complete the same job. If x = 4y, by what percent will x have to decrease so that A and B together
can complete the job in 3y/8 hours?
(A) 15%
(B) 25%
(C) 30%
(D) 62.5%
(E) 85%

How can we solve it by picking numbers?
OA E
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by Brent@GMATPrepNow » Tue Aug 25, 2015 7:49 pm
tapanmittal wrote:Machine A currently takes x hours to complete a certain job. Machine B currently takes y hours to
complete the same job. If x = 4y, by what percent will x have to decrease so that A and B together
can complete the job in 3y/8 hours?
(A) 15%
(B) 25%
(C) 30%
(D) 62.5%
(E) 85%
Here's an approach that minimizes that calculations required.

First, let y = 1
In other words, Machine B takes 1 hour to complete the job.

If x = 4y, then x = 4(1) = 4
So, Machine A takes 4 hours to complete the job.

We want A and B, working together, to complete the job in 3y/8 hours.
Since y = 1, we want their time to be 3(1)/8 hours.
So, working together, they need to complete the job in 3/8 hours.

IMPORTANT
At the moment, x = 4 (Machine A takes 4 hours to complete the job.)
Let's see what happens if we decrease x by 75%. When we do this, we get 1
In other words, Machine A takes 1 hour to complete the job.

So, if Machine A takes 1 hour to complete the job, and Machine B takes 1 hour to complete the job, then working together, they will complete the job in 1/2 hour.

However, we need them to complete the job in 3/8 hours (we need them to complete the job even faster than 1/2 an hour)
So, we need to decrease the value of x by MORE THAN 75%

Since only answer choice E is greater than 75%, it must be the correct answer.

Cheers,
Brent
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by GMATGuruNY » Wed Aug 26, 2015 3:22 am
tapanmittal wrote:Machine A currently takes x hours to complete a certain job. Machine B currently takes y hours to complete the same job. If x = 4y, by what percent will x have to decrease so that A and B together can complete the job in 3y/8 hours?
(A) 15%
(B) 25%
(C) 30%
(D) 62.5%
(E) 85%
Since the job must be completed in 3y/8 hours, let y = 8 hours, implying that x = 4y = 4*8 = 32 hours and that the shorter time = 3y/8 = (3*8)/8 = 3 hours.
Let the job = the LCM of 8, 32 and 3 = 96 widgets.

Regular times:
Since A takes 32 hours to complete the job, A's rate = w/t = 96/32 = 3 widgets per hour.
Since B takes 8 hours to complete the job, B's rate = w/t = 96/8 = 12 widgets per hour.

Shorter time:
At a rate of 12 widgets per hour, the number of widgets produced by B in 3 hours = rt = 12*3 = 36 widgets.
Since B produces 36 of the 96 widgets, the number of widgets produced by A in 3 hours = 96-36 = 60 widgets.

At A's normal rate of 3 widgets per hour, the normal time for A to produce 60 widgets = w/r = 60/3 = 20 hours.

Percent decrease change in A's time to produce 60 widgets:
(normal time - faster time)/(normal time) = (20-3)/20 = 17/20 = 85/100 = 85%.

The correct answer is E.
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