Question

How many in a group are women with blue eyes?
(1) Of the women in the group, 5 percent have blue eyes.
(2) Of the men in the group, 10 percent have dark-colored eyes.

• 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 Data Sufficiency questions that ask for a specific value (e.g., "how many," "what is the value of"), providing only a percentage or a ratio is not enough. You must be able to calculate a single numerical answer.

Answer 1

Answer: (E)

Step 1: Understanding the Question
The question asks for a specific number: the count of women with blue eyes. Let W be the total number of women in the group. We need to find the value of \(0.05 \times W\).
Step 2: Analysis of Statement (1)
Statement (1) tells us that 5% of the women have blue eyes. This gives us the proportion but not the actual number. The number of women with blue eyes is \(0.05 \times W\). Since we do not know the value of W (the total number of women), we cannot determine the specific number of women with blue eyes.
For example, if there are 100 women, then 5 have blue eyes. If there are 200 women, then 10 have blue eyes. We cannot find a unique answer.
Therefore, Statement (1) ALONE is not sufficient.
Step 3: Analysis of Statement (2)
Statement (2) provides information about the men in the group (10% have dark-colored eyes). This information is completely unrelated to the number of women with blue eyes.
Therefore, Statement (2) ALONE is not sufficient.
Step 4: Analysis of Statements (1) and (2) Together
Combining both statements does not provide any new information to help solve the problem. We have a percentage for women (from statement 1) and a percentage for men (from statement 2), but we don't know the total number of women, the total number of men, or the total number of people in the group. There is no link between the two pieces of information.
Therefore, Statements (1) and (2) TOGETHER are not sufficient.
Step 5: Final Answer
Since neither statement alone nor both statements together are sufficient to answer the question, the correct answer is (E).