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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 condition on its own first.
Condition 1)
Since the sum of 2, 3, 4, 5 and 6 is 20, which is an even number, and n=5 is an odd number, the answer is sometimes 'no'.
Since the sum of 1, 2, 3, and 4 is 10, which is an even number, and n=4 is an even number, the answer is sometimes 'yes'.
Condition 1) is not sufficient since it does not yield a unique answer.
Condition 2)
If n = 4, then [n/2] = 2 is even, and n is even.
If n = 5, then [n/2] = 2 is also even, but n is not even.
Condition 2) is not sufficient since it does not yield a unique answer.
Conditions 1) & 2)
Since the sum of 2, 3, 4, 5 and 6 is 20, which is an even number, and n=5 is an odd number such that [n/2] = 2 is even, the answer is sometimes 'no'.
Since the sum of 1, 2, 3, and 4 is 10, which is an even number, and n=4 is an even number such that [n/2] = 2 is even, the answer is sometimes 'yes'.
Conditions 1) & 2) together are not sufficient, since they do not yield a unique answer.
Therefore, E is the answer.
Answer: E
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.
