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GRE Quantitative Reasoning
QUESTION #8074
Question 1
$n$ is an even integer and a multiple of 3.
Compare:
Column A: The remainder when $n$ is divided by 12
Column B: 6
Correct Answer Explanation
Since $n$ is even and a multiple of 3, $n$ must be a multiple of $\text{lcm}(2, 3) = 6$.
So $n = 6k$ for some integer $k$.
When we divide $n = 6k$ by 12:
- If $k$ is even (say $k = 2m$): $n = 12m$, remainder = 0
- If $k$ is odd (say $k = 2m + 1$): $n = 6(2m + 1) = 12m + 6$, remainder = 6
So the remainder when $n$ is divided by 12 can be either 0 or 6.
Since Column A could be 0 (less than 6) or 6 (equal to 6), the relationship cannot be determined.
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