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Is the integer k divisible by 4 ? (1) 8k is divisible by 16

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Source: — Data Sufficiency |
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by deloitte247 » Sun Oct 20, 2019 1:33 am
Statement 1=> 8k is divisible by 16.
$$\frac{8k}{16}=\frac{k}{2}$$
Hence, k is a multiple of 2
If k=6, then k is not divisible by 4
If k=8, then k is divisible by 4
The information provided is not enough to arrive at a definite answer, hence statement 1 is NOT SUFFICIENT.

Statement 2=>
9k is divisible by 12
$$\frac{9k}{12}=\frac{3k}{4}\ =\ \frac{3}{1}\cdot\frac{k}{4}$$
Hence, k is a multiple of 4.
If k=8, then k is divisible by 4
If k=12, then k is divisible by 4
Hence, statement 2 is SUFFICIENT.

Since statement 2 alone is SUFFICIENT, the answer is, therefore, option B.
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