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
DS - Machine X and Machine Y Rate Problem
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Statement 1: X produced 30 bottles per minute.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
Thus, the work produced by X in 240 minutes = r*t = 30*240.
No information about how much work was produced by Y.
INSUFFICIENT.
Statement 2: Machine X produced twice as many bottles in 4 hours as Machine Y produced in 3 hours.
Thus, for every bottle Y produced, X produced 2 bottles, implying that X produced 2 of every 3 bottles.
Since X produced 2/3 of the lot in 4 hours, X would need 2 more hours to produce the remaining 1/3 of the lot, for a total of 6 hours.
SUFFICIENT.
The correct answer is B.
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- Jay@ManhattanReview
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Hi TxGMAT,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 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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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.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
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
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