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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.
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The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.
9^1 = 9, 9^2 = 81 ~ 1, 9^3 = 729 ~ 9, 9^4 ~ 1, …
The odd number powers of 9 have the units digit 9 and the even number powers of 9 have the units digits 1.
Condition 1) tells us that n is an even number and 9^n – 1 ~ 1 – 1 = 0.
Thus condition 1) is sufficient.
Condition 2)
If n = 3, then we have 9^3 – 1 ~ 9 – 1 = 8. However, if n = 6, then we have 9^6 – 1 ~ 1 – 1 = 0. Therefore, condition 2) does not yield a unique solution.
Condition 2) is not sufficient.
Therefore, A is the answer.
Answer: A
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.
