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Machines A, B and C produce identical balls at their

by BTGmoderatorLU » Tue Dec 11, 2018 2:51 pm
Source: e-GMAT

Machines A, B and C produce identical balls at their respective constant rates. If machines A and B operating simultaneously can produce a batch of balls in 4 hours and 48 minutes, in how much time can machines A and C operating simultaneously produce the same batch of balls?

1) Machines A, B and C operating simultaneously can produce the same batch of balls in 24/11 hours.
2) Machine B operating alone takes 50 percent more time to produce the same batch of balls than Machine A operating alone.

The OA is C.
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by Jay@ManhattanReview » Tue Dec 11, 2018 9:22 pm
BTGmoderatorLU wrote:Source: e-GMAT

Machines A, B and C produce identical balls at their respective constant rates. If machines A and B operating simultaneously can produce a batch of balls in 4 hours and 48 minutes, in how much time can machines A and C operating simultaneously produce the same batch of balls?

1) Machines A, B and C operating simultaneously can produce the same batch of balls in 24/11 hours.
2) Machine B operating alone takes 50 percent more time to produce the same batch of balls than Machine A operating alone.

The OA is C.
Say Machines A, B and C, working individually, produce the same batch of balls in a, b, and c hours.

Given that machines A and B operating simultaneously can produce a batch of balls in 4 hours and 48 minutes = 24/5 hours

Thus, as per the information, we have,

1/a + 1/b = 1/(24/5) => 1/a + 1/b = 5/24 ---(1)

We have to get the value of reciprocal of (1/a = 1/b).

Let's take each statement one by one.

1) Machines A, B and C operating simultaneously can produce the same batch of balls in 24/11 hours.

1/a + 1/b + 1/c = 1/(24/11) => 1/a + 1/b + 1/c = 11/24 ---(2)

But we can't get the value of 1/a + 1/c even with the help of eqn (1), though we can get the value of 1/c.

From eqn (1) and (2), we have (1/a + 1/b + 1/c) - (1/a + 1/b) = 11/24 - 5/24 = 6/24 = 1/4

=> 1/c = 1/24. Insufficient.

2) Machine B operating alone takes 50 percent more time to produce the same batch of balls than Machine A operating alone.

=> b = 1.5a. Insufficient

(1) and (2) together

From eqn (1), we have 1/a + 1/(1.5a) = 5/24 =>2.5/a = 5/24 => 1/a = 1/12

Thus, 1/a + 1/c = 1/12 + 1/24 = 3/24 = 1/8

=> Machines A and C operating simultaneously produce the same batch of balls in reciprocal of 1/8 = 8 hours. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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