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What is the units digit of 3^n?

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What is the units digit of 3^n?

by Max@Math Revolution » Mon Aug 12, 2019 11:44 pm

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[GMAT math practice question]

What is the units digit of 3^n?

1) n is a multiple of 4
2) n is a multiple of 6
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Source: — Data Sufficiency |
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by Max@Math Revolution » Thu Aug 15, 2019 5:26 pm

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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. We should simplify the conditions if necessary.

The units digits of 3^n for n = 1, 2, 3, 4, ... are 3, 9, 7, 1, 3, 9, 7, 1, ...
So, the units digits of 3^n have period 4:
They form the cycle 3 -> 9 -> 7 -> 1.
Thus, 3^n has a units digit of 1 if n is a multiple of 4.

Note that 6 is not a multiple of 4.

Therefore, A is the answer.
Answer: A
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