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

Since we have 1 variable and 0 equation, D is most likely to be the answer. According to CMT4(B), if D is chosen as an answer too easily for key area questions, we should check the answer A or B. This question is about integers, which is one of the key question areas.

Condition 1)

n^2 = 2*3*k for an integer.

Since 2 and 3 are prime factors of n^2, 2 and 3 are prime factor of n.

Thus, 2*3 = 6 is a factor of n.

This is sufficient.

Condition 2)

We have two cases as follows.

n = 3 does not have 6 as a factor.

n = 12 has 6 as a factor.

This is not sufficient.

Therefore, the answer is A.

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both con 1) and con 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Thus, D is most likely to be the answer using con 1) and con 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

Answer: A

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