2IIM

Hi

The following data sufficiency question is a question that tests your knowledge about number of factors for a number.

Directions to answer the DS question
1. Statement (A) ALONE is sufficient, but statement (B) alone is not sufficient to answer the question asked.
2. Statement (B) ALONE is sufficient, but statement (A) alone is not sufficient to answer the question asked.
3. BOTH statements (A) and (B) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
4. EACH statement ALONE is sufficient to answer the question asked.
5. Statements (A) and (B) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Question

How many factors does the number 'x' have?
A. 3x has 3 factors.
B. x^2 has 3 factors

Correct Answer
Choice (4). EACH statement ALONE is sufficient to answer the question asked.

Explanatory Answer

Statement A

3x has 3 factors. Perfect squares have odd number of factors. Therefore, 3x has to be a perfect square.

The only option that 3x can take is '9' that will satisfy the condition that 3x has 3 factors.
Hence, x is 3. 3 has 2 factors.

So, we can answer question using statement A.

Statement B

x^2 has 3 factors.
The factors will be 1, x and x^2. Hence, x has to be the only prime factor of x^2.
As x is a prime number, it has exactly 2 factors.

We have been able to answer the question using statement B also.

As we could answer the question using each statement alone, correct answer is choice (4).

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