Question

What is the probability that a randomly chosen student from a class is a girl?
(1) There are 30 students in the class.
(2) The ratio of boys to girls in the class is 2:3.

• 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 probability questions in Data Sufficiency, remember that you often need a ratio, not necessarily the absolute numbers. If a statement provides the ratio of the parts, you can usually find the probability.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This is a Data Sufficiency question about probability. To find the probability of selecting a girl, we need to know the ratio of the number of girls to the total number of students. The formula is:
\[ P(\text{Girl}) = \frac{\text{Number of Girls}}{\text{Total Number of Students}} \]
Step 2: Detailed Explanation:
Analyze Statement (1):
"There are 30 students in the class."
This tells us the Total Number of Students is 30. However, we do not know the Number of Girls. The probability is \(\frac{\text{Number of Girls}}{30}\), which cannot be determined. Thus, statement (1) is not sufficient.
Analyze Statement (2):
"The ratio of boys to girls in the class is 2:3."
This means that for every 2 boys, there are 3 girls. We can represent the number of boys as \(2k\) and the number of girls as \(3k\), where \(k\) is a positive integer.
The Total Number of Students is \(2k + 3k = 5k\).
The probability of choosing a girl is:
\[ P(\text{Girl}) = \frac{\text{Number of Girls}}{\text{Total Number of Students}} = \frac{3k}{5k} = \frac{3}{5} \]
The unknown \(k\) cancels out, giving us a single, unique value for the probability. Thus, statement (2) is sufficient.
Step 3: Final Answer:
Statement (2) alone is sufficient to answer the question, but statement (1) alone is not. This corresponds to option (B).