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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.

Modifying the question:
The question asks if √17n = a for some integer a. This is equivalent to asking if 17n = a^2 for some integer a.

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 68n is the square of an integer and 68 = 4*17, we must have 68n = 4*17*17*k^2 for some integer k, and n = 17*k^2 or 17n = 17^2*k^2 = (17*k)^2.
Thus, 17n is the square of the integer 17k, and condition 1) is sufficient.

Condition 2)
Since n/68 is a square of an integer and 68 = 4*17, we have n/68 = m^2 for some integer m, and n = 17*4*m^2 or 17n = 17^2*2^2*m^2 = (34m)^2.
Thus, 17n is the square of the integer 17k, and condition 2) is sufficient.

Therefore, D is the answer.
Answer: 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.