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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

  • Column A is greater
  • Column B is greater
  • The two quantities are equal
  • The relationship cannot be determined✔️
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.