DS - Machine X and Machine Y Rate Problem

TxGMAT wrote:Machine X and Y produced identical bottles at different constant rates. Machine X, operating alone for four hours, filled part of a production lot; then Machine Y, operating alone for three hours, finished the lot. How many hours would it have taken machine X operating alone to fill the entire production lot?

(1) Machine X produced 30 bottles/minute
(2) Machine X produced twice as many bottles in four hours as Machine Y produced in 3 hours

Hi TxGMAT,

We have: Machine X worked for 4 hours and did some part of the job, and then machine Y worked for 3 hours and did the remaining part of the job.

If we get to know either the part of the job done by machine X or the part of the job done by machine Y, we get the unique answer.

Statement 1: Machine X produced 30 bottles/minute

This is clearly insufficient; there is no information either about the part of job machine X did or about the rate at which machine Y worked.

Statement 2: Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours

The statement implies that while working for 4 hours, machine X did 2/3rd of the job, machine Y did the 1/3rd of the job.

This is exactly what the question describes.

Since machine X takes 4 hours to do 2/3rd of the job, it would take 4/2 = 2 hours to do the remaining (1/3rd) part of the job.

Thus, the total time taken by machine X to do the complete job = [spoiler]4 + 2 = 6 hours[/spoiler]ours.

The correct answer: B

Hope this helps!

Relevant book: Manhattan Review GMAT Word Problems Guide

-Jay
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TxGMAT wrote:Machine X and Y produced identical bottles at different constant rates. Machine X, operating alone for four hours, filled part of a production lot; then Machine Y, operating alone for three hours, finished the lot. How many hours would it have taken machine X operating alone to fill the entire production lot?

(1) Machine X produced 30 bottles/minute
(2) Machine X produced twice as many bottles in four hours as Machine Y produced in 3 hours

We are given that Machines X and Y produced identical bottles and that Machine X worked for 4 hours filling part of the lot and Machine Y worked for 3 hours filling the rest of the lot. If we let the rate of Machine X in bottles per hour be X and the rate of Machine Y in bottles per hour be Y, we can determine the amount of work done by Machine X and by Machine Y.

rate x time = work

Work done by Machine X = X * 4 = 4X

Work done by Machine Y = Y * 3 = 3Y

Thus, the total work completed = 4X + 3Y.

We need to determine how long it would take Machine X to fill the entire lot. Since the work needed to produce the entire lot is 4X + 3Y and time = work/rate, we can use the following equation to determine the time of Machine X:

Time for Machine X to fill the entire lot = (4X + 3Y)/X

Statement One Alone:

Machine X produced 30 bottles per minute.

This means Machine X produced 30 x 60 = 1800 bottles per hour. Although we know the rate of Machine X, we do not have enough information to determine how long it will take Machine X to fill the entire lot. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

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

From the given information, we know that work of Machine X = 4X and that work of Machine Y = 3Y. Using those two work values and the information in statement two, we can create the following equation:

4X = 2(3Y)

4X = 6Y

2X = 3Y

Since 2X = 3Y, we can substitute 2X for 3Y in the expression (4X + 3Y)/X. Thus, we have:

(4X + 2X)/X

6X/X

6 = Time for Machine X to fill the entire lot

Statement two alone is sufficient to answer the question.

Answer: B