BTGmoderatorDC wrote:Machines X and Y produced identical bottles at different constant rates. Machine X, operating alone for 4 hours, filled part of a production lot; then Machine Y, operating alone for 3 hours, filled the rest of this lot. How many hours would it have taken Machine X operating alone to fill the entire production lot?

(1) Machine X produced 30 bottles per minute.
(2) Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours.

OA B

Source: Official Guide

Say

Machine X filled X bottles in 4 hours; thus, Machine X's rate = X/4 bottles per hour; and
Machine Y filled X bottles in 3 hours; thus, Machine Y's rate = Y/3 bottles per hour

We have to find out in how many hours will Machine X will fill (X + Y) bottles. It will take (4 + 4Y/X) hours.

If we get the value of Y/X, we get the answer.

Question rephrased: What's the value of Y/X?

Let's take each statement one by one.

(1) Machine X produced 30 bottles per minute.

No information about Machine Y. Insufficient.

(2) Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours.

=> X = 2Y => Y/X = 1/2. Sufficient.

Machine X will take 4 + 4Y/X = 4 + 4*(1/2) = 6 hours fill the entire production lot.

The correct answer: B

Hope this helps!

-Jay
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