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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.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)

Since \(91 = 7*13\), \(n^2\) is a multiple of both \(7\) and \(13\). Since \(7\) and \(13\) are prime numbers, \(n\) must be a multiple of both \(7\) and \(13\).

Condition 1) is sufficient.

Condition 2)

If \(91\) is a factor of \(2n\), then \(91k = 2n\) for some integer \(k\). Since \(91\) is odd, \(k\) must be an even integer. Write \(k = 2a\), for some integer \(a\). Then

\(2n = 91*2a\). It follows that \(n = 91*a\).

Thus, \(n\) is a multiple of \(91\).

Condition 2) is sufficient.

This is a CMT(Common Mistake Type) 4(B) question. Condition 2) is easy to understand and condition 1) is difficult to figure out. If you are unable to figure out condition 2), you should choose D as the answer.

Therefore, the answer is D.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A, B, C or E.

Answer: D

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