EgmatQuantExpert wrote:

Question:

If \(N\)\(\) is a positive integer, is \(N^3/4\) an integer?

1. \(N^2+3\) is a prime number.

2. \(N\) is the number of odd factors of \(6\).

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) Statement (1) and (2) TOGETHER are NOT sufficient.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

We can modify the original condition and question as follows.

The question that \(N^3/4\) is an integer is equivalent to \(N\) is an even integer.

Condition 1)

In order for \(N^2 + 3\) to an prime number, \(N^2\) and \(N\) must be an even integer.

The condition 1) is sufficient.

Condition 2)

\(N = 1\) or \(N = 3\).

For both cases, \(N^3/4\) is \(1/4\) or \(27/4\).

They are not integers.

Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, the condition 2) is sufficient.

Therefore, D is the answer.

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