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 Question:
The main question asks for a specific positive number. The property of the number is that it is divisible by both 3 and 4. A number divisible by both 3 and 4 must be a multiple of their Least Common Multiple (LCM).
Step 2: Key Formula or Approach:
The LCM of 3 and 4 is 12. So, the number must be a multiple of 12. The possible numbers are 12, 24, 36, 48, and so on. We need to check if the given statements can uniquely identify one of these numbers.
Step 3: Detailed Explanation:
Analyze Statement I alone:
Statement I says, "It is greater than 15". The multiples of 12 that are greater than 15 are 24, 36, 48, ... Since we get multiple possible numbers, Statement I alone is not sufficient to answer the question.
Analyze Statement II alone:
Statement II says, "It is less than 14". The only positive multiple of 12 that is less than 14 is 12. This statement gives a unique answer. Therefore, Statement II alone is sufficient to answer the question.
Conclusion:
The question can be answered by using Statement II alone, but not by using Statement I alone. This corresponds to option (a).
Step 4: Final Answer:
The correct choice is (a) as the question can be answered by one of the statements alone (Statement II) and not by the other.