Question: Working together at their constant rates, pumps X and Y fill an empty pool to capacity in 1/3 hours. How many minutes does it take pump Y, working alone, to fill the pool?

1. The capacity of the pool is 900 gallons
2. The rate of Pump X is 30 gallons per minute

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer:
Solution with Explanation:
Approach Solution (1):

Rate * Time = Job
We are told that (x + y) * 20 = c, where x is the rate of pump X in gallons per minute, y is the rate of pump Y in gallons per minute and c is the capacity of the pool in gallons
The question asks to find the value of y

1.The capacity of the pool is 900 gallons
c = 900, hence we have that (x + y) * 20 = 900, so x + y = 45
Not sufficient

2.The rate of pump X is 30 gallons per minute. x = 30, hence we have that (30 + y) * 20 = c. We have two unknowns and only one equation.
Not sufficient
(1) + (2) x = 30 and x + y = 45. Solving gives y = 15
Sufficient

Correct Option: C

Approach Solution (2):

Working together at their constant rates, pumps X and Y can fill an empty pool to capacity in 1/3 hours.

1.The capacity of the pool is 900 gallons
The capacity is given, we know the combined time, so we know the combined speed = 900/20 = 45 l/min but nothing can be said about speed or time taken
Insufficient

2.The rate of Pump X is 30 gallons per minute
We know only speed of pump X, but nothing on time taken
Insufficient

Combined, we know X speed is 30 g/min and speed combined is 45 g/m
So Y’s speed = 15 g/m
Time taken by Y = 900/15 = 60 minutes
Sufficient

Correct Option: C

Approach Solution (3):

S1: The capacity of the pool is 900 gallons
The capacity is given, we know the combined time, so we know the combined speed = 900/20 = 45 l/min but nothing can be said about speed or time taken
Not sufficient

S2: The rate of pump X is 30 gallons per minute
x = 30, hence we have that (30 + y) * 20 = c. we have two unknowns and only one equation
Not sufficient

Correct Option: C

“Working together at their constant rates, pumps X and Y fill an empty pool to capacity in 1/3 hours. How many minutes does it take pump Y, working alone, to fill the pool?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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