Question

A certain cafeteria sells donuts and pizzas. Is the number of people who bought donuts more than the number of people who bought pizzas?
(1) Of the people who bought donuts, 30 percent of them also bought pizzas.
(2) Of the people who bought pizzas, 40 percent of them also bought donuts.

• A. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
• B. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
• C. Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.
• D. Each statement alone is sufficient to answer the question.
• E. Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.

Hint:

When given percentage information, make sure to look for specific quantities to find a direct relationship between the variables.

Answer 1

Answer: (E)

Step 1: Analyze Statement 1.
Statement 1 tells us that 30 percent of people who bought donuts also bought pizzas, but this doesn't give us the total number of people who bought donuts or pizzas. We don't know how many people bought donuts or how many bought pizzas, so statement 1 alone is insufficient.
Step 2: Analyze Statement 2.
Statement 2 tells us that 40 percent of people who bought pizzas also bought donuts, but again, we do not know the total number of people who bought either donuts or pizzas. Therefore, statement 2 alone is also insufficient.
Step 3: Combine Both Statements.
Combining both statements, we still don't know the total numbers of people who bought donuts or pizzas. Thus, we cannot determine if the number of people who bought donuts is greater than the number of people who bought pizzas.
Step 4: Conclusion.
The correct answer is (E).