Question

The total cost of food for the raccoons at the Altadena Wildlife Rescue has increased as the number of raccoons at the Rescue has increased. If it costs the same amount to feed each raccoon, is the cost of food for 7 raccoons more than $2,000 annually?
(1) It costs more than $1,000 annually to feed 4 raccoons.
(2) It costs more than $1,500 annually to feed 5 raccoons.

• 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:

For Yes/No Data Sufficiency questions involving inequalities, rephrase the main question into a simpler inequality (e.g., "Is C>285.71?"). Then, for each statement, check if the resulting inequality guarantees a "Yes" or a "No" answer to your rephrased question.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This Data Sufficiency question is a "Yes/No" question. We need to determine if the cost for 7 raccoons is greater than \$2000. A statement is sufficient if it allows us to answer with a definitive "Yes" or a definitive "No".
Step 2: Key Formula or Approach:
Let \(C\) be the annual cost to feed one raccoon.
The question asks: Is \(7 \times C>2000\)?
This can be simplified by dividing by 7: Is \(C>\frac{2000}{7}\)?
\( \frac{2000}{7} \approx 285.71 \). So, the question is: Is \(C>285.71\)?
Step 3: Detailed Explanation:
Analyzing Statement (1):
"It costs more than $1,000 annually to feed 4 raccoons."
This gives us the inequality: \(4C>1000\).
Dividing by 4, we get: \(C>250\).
Does knowing that \(C>250\) definitively answer if \(C>285.71\)? No.
For example, \(C\) could be 260. In this case, \(C\) is not greater than 285.71 (Answer: No).
Or, \(C\) could be 300. In this case, \(C\) is greater than 285.71 (Answer: Yes).
Since we can get both a "Yes" and a "No", statement (1) is not sufficient.
Analyzing Statement (2):
"It costs more than $1,500 annually to feed 5 raccoons."
This gives us the inequality: \(5C>1500\).
Dividing by 5, we get: \(C>300\).
Does knowing that \(C>300\) definitively answer if \(C>285.71\)? Yes.
Since every possible value of \(C\) is greater than 300, it must also be greater than 285.71.
This statement gives us a definitive "Yes" answer. Therefore, statement (2) alone is sufficient.
Step 4: Final Answer:
Statement (2) alone is sufficient to answer the question, but statement (1) alone is not.