Data Sufficiency

[Math Revolution GMAT math practice question]

What is the remainder when 2^n is divided by 10?

1) n is a positive multiple of 2
2) n is a positive multiple of 4

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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.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

The remainder when 2^n is divided by 10 is the units digit of 2^n.

Now, 2^1 = 2, 2^2 = 4, 2^3 = 8, 2^4 = 16, and 2^5 = 32.
So, the units digits of 2^n have period 4:
They form the cycle 2 -> 4 -> 8 -> 6.
Thus, 2^n has the units digit of 6 when n is a multiple of 4.
Condition 2) is sufficient.

Condition 1)
If n = 4, then 2^n = 2^4 = 16 has the units digit of 6.
If n = 2, then 2^n = 2^2 = 4 has the units digit of 4.
Since we don't have a unique solution, condition 1) is not sufficient.

Therefore, B is the answer.

Answer: B