Last Updated on May 9, 2023
GMAT OFFICIAL GUIDE DS
Solution:
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
