Machine A currently takes x hours to complete a certain job

[guerrero]

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%

source .MGMAT


OA
E

[Brent@GMATPrepNow]

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%

source .MGMAT


OA
E

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

[GMATGuruNY]

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%
E

Time for Machine B:
So that 3y/8 is an integer value, let y = 8 hours.

Time for Machine A:
x = 4y = 4*8 = 32 hours.

Let the job = the LCM of 8, 3 and 32 = 96 units.
Rate for B = w/y = 96/8 = 12 units per hour.
Rate for A = w/x = 96/32 = 3 units per hour.

To complete the job in 3y/8 = 3 hours, the required rate for A and B together = 96/3 = 32 units per hour.
Since B produces 12 units per hour. A must produce the balance:
32-12 = 20 units per hour.
Thus, A's new time = w/(new rate) = 96/20 = 48/10 = 4.8 hours.

Decrease in A's time = 32-4.8 = 27.2 hours.
Since 75% of 32 = 24 hours, A's time decreases by MORE THAN 75%.

The correct answer is E.