Question

If a certain city is losing 12 percent of its daily water supply each day because of water-main breaks, what is the dollar cost to the city per day for this loss?
(1) The city's daily water supply is 350 million gallons.
(2) The cost to the city for each 12,000 gallons of water lost is \$2.

• 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 problems, first identify exactly what pieces of information are needed to answer the question. For a cost calculation, you almost always need both a quantity (how much?) and a rate (how much per unit?). Check if each statement provides one of these pieces.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This is a Data Sufficiency question. The goal is to determine if the information provided in the statements is sufficient to answer the question, not to find the actual numerical answer itself. We need to find the total dollar cost per day.
Step 2: Analyzing the Question Stem:
The question asks for the total dollar cost of the water loss per day.
From the stem, we know:
Water loss = 12% of the daily water supply.
To find the total cost, we need two key pieces of information:
1. The total volume of water lost per day.
2. The cost per unit volume of water.
Total Cost = (Volume of water lost) \(\times\) (Cost per unit volume)
Step 3: Detailed Explanation:
Evaluating Statement (1) Alone:
"The city's daily water supply is 350 million gallons."
This statement allows us to calculate the total volume of water lost.
\[ \text{Volume Lost} = 12% \times 350,000,000 \text{ gallons} = 0.12 \times 350,000,000 = 42,000,000 \text{ gallons} \] However, we do not know the cost of this water. We cannot determine the total dollar cost.
Therefore, Statement (1) alone is not sufficient.
Evaluating Statement (2) Alone:
"The cost to the city for each 12,000 gallons of water lost is \$2."
This statement gives us the cost per unit volume.
\[ \text{Cost Rate} = \frac{\$2}{12,000 \text{ gallons}} \] However, we do not know the total daily water supply, so we cannot calculate the total volume of water lost (12% of an unknown number).
Therefore, Statement (2) alone is not sufficient.
Evaluating Statements (1) and (2) Together:
Using both statements, we have all the information needed.
- From Statement (1), the total volume of water lost is 42,000,000 gallons.
- From Statement (2), the cost is \$2 for every 12,000 gallons.
We can now calculate the total daily cost:
\[ \text{Total Cost} = (\text{Total Gallons Lost}) \times (\text{Cost per Gallon}) \] \[ \text{Total Cost} = 42,000,000 \text{ gallons} \times \frac{\$2}{12,000 \text{ gallons}} = \frac{42,000,000 \times 2}{12,000} = \$7,000 \] Since we can find a single, unique value for the total cost, the two statements together are sufficient.
Step 4: Final Answer:
Neither statement is sufficient on its own, but together they provide enough information to solve the problem. This corresponds to option (C).