Question

What is the ratio of men to women rolled in a certain class?

1. The number of women enrolled in the class is 3 less than half the number of men enrolled.
2. The number of women enrolled in the class is $\frac 25$ of the number of men enrolled.

This questions has a problem and two statements, number I and II. Decide if the information given in the statement is sufficient for answering the problem. Mark the answer:

• A. Statement I by itself is sufficient to answer the question, but statement II by itself is not.
• B. Statement II by itself is sufficient to answer the question, but statement I by itself is not.
• C. Statements I and II taken together are sufficient to answer the question, even though neither statement by itself is sufficient.
• D. Either statement by itself is sufficient to answer the question.

Answer 1

Answer: (B)

Statement II by itself is sufficient to answer the question, but statement I by itself is not.

Answer 2

Statement I provides a more complex relationship :
$w = \frac{1}{2}m - 3$
This relationship alone does not directly give a simple ratio because it involves subtraction, making it impossible to immediately find a proportional ratio.
Statement II provides a clear, direct proportion :
$w = \frac {2}{5}m$
which immediately leads to a ratio of $m:w = 5:2$. Hence, Statement II is sufficient on its own.

So, the correct option is (B): If statement II by itself is sufficient to answer the question, but statement I by itself is not.