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If n = 3k, is k an integer?

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Source: — Data Sufficiency |
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If n = 3k, is k an integer?

by Vincen » Sat Apr 20, 2019 3:52 am
If n = 3k, is k an integer?

(1) n is an integer.
(2) n/6 is an integer.

OA=B

Source: GMAT Prep
Hi Vjesus12.

We need to determine if k is an integer or not. So, let's do it.

First, let's rewrite the given expression as $$n=3k\ \ \ \ \Rightarrow\ \ \ k=\frac{n}{3}.$$ Statement 1
(1) n is an integer.
We have two cases:

(i) If n is a multiple of 3, then k is an integer.
(ii) If n is not a multiple of 3 (for example, n=2), then k is not an integer.

So, this statement is NOT SUFFICIENT.

Statement 2
(2) n/6 is an integer.
Here we have that $$\frac{n}{6}=p\ \ \ \Rightarrow\ n=6\cdot p\ \ \ \ \Rightarrow\ \ \ n=3\cdot2\cdot p,\ \ \ \ \ \ p\in\mathbb{Z}.$$ So, we get $$k=\frac{n}{3}=\frac{3\cdot2\cdot p}{3}=2\cdot p\ \in\mathbb{Z}\ \ .$$ So, k is an integer. Therefore, this statement is SUFFICIENT.

Hence, the correct answer is the option _B_.

I hope it helps you.
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