Question

During a particular period, water enters a partially filled reservoir at a constant rate through a mountain stream. At the same time, water is pumped out of the reservoir at a constant rate through an outlet pipe. At what rate, in gallons per minute, is the amount of water in the reservoir increasing?
(1) The amount of water initially in the reservoir is 1800 gallons.
(2) Water is pumped into the reservoir at a rate of 8 gallons per minute and out of the reservoir at a rate of 20 gallons every 3 minutes.

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• D. EACH statement ALONE is sufficient.
• E. Statements (1) and (2) TOGETHER are NOT sufficient.

Hint:

In data sufficiency questions about rates, focus on what information is needed to calculate the final rate. Initial quantities are often distractors unless the question asks for a quantity at a specific time. Always ensure that the units of all rates are consistent before performing any calculations.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The question asks for the net rate at which the amount of water in the reservoir is increasing. This is a classic rate problem. The net rate is the difference between the rate of water flowing in and the rate of water being pumped out.
Net Rate = (Rate of water in) - (Rate of water out)
Step 2: Detailed Explanation:
Analyzing Statement (1):
This statement provides the initial volume of water in the reservoir, which is 1800 gallons.
This information is a starting condition, but it tells us nothing about the rates of flow in or out.
Therefore, statement (1) alone is not sufficient to answer the question.
Analyzing Statement (2):
This statement provides the necessary rates.
Rate of water in = 8 gallons per minute.
Rate of water out = 20 gallons every 3 minutes.
We need to express the rate out in gallons per minute to match the units of the rate in.
\[ \text{Rate of water out} = \frac{20 \text{ gallons}}{3 \text{ minutes}} \]
Now, we can calculate the net rate of increase:
\[ \text{Net Rate} = \text{Rate in} - \text{Rate out} = 8 - \frac{20}{3} \]
\[ \text{Net Rate} = \frac{24}{3} - \frac{20}{3} = \frac{4}{3} \text{ gallons per minute} \]
Since we can find a unique value for the rate of increase using this statement, statement (2) alone is sufficient.
Step 3: Final Answer:
Statement (2) alone is sufficient to determine the rate of increase, while statement (1) alone is not. Therefore, the correct option is (B).