Question

A positive number is exactly divisible by 4 and 3 both. What is that number?
I. It is greater than 15
II. It is less than 14

• A. Option a
• B. Option b
• C. Option c
• D. Option d

Hint:

In Data Sufficiency, always check each statement individually first. Only if neither statement is sufficient alone should you proceed to check them combined.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
A number divisible by both 4 and 3 must be a multiple of their Lowest Common Multiple (LCM).
\[ \text{LCM}(3, 4) = 12 \] The positive numbers divisible by 12 are \( \{12, 24, 36, 48, ...\} \).
Step 2: Detailed Explanation:
The question asks "What is that number?", implying we need a unique value.
Statement I: The number is greater than 15.
Possible values are \( \{24, 36, 48, ...\} \). This does not provide a single unique answer.
Statement II: The number is less than 14.
The only positive multiple of 12 less than 14 is 12. This provides a unique answer.
According to the directions:
a) If the question can be answered by one of the statements alone and not by the other.
Since Statement II alone answers the question and Statement I does not, condition (a) is satisfied.
Step 3: Final Answer:
The answer is Option a.