If k and n are positive integers, is k a factor of 3n

Question

If k and n are positive integers, is k a factor of 3n?

Given: n is a multiple of k.

(a) Yes always
(b) No, never
(c) Sometimes yes, sometimes no

During a tutorial video, the instructor says the correct answer would be a but I would like to discuss the case where n is 0. If n is 0, this means that n is a multiple of k since 0 is a multiple of any given number. Nevertheless, this would not mean that k is a factor of 3n since 0 is not a factor of any number except 0. Thus, the correct answer would be (c).

Can someone help me understand which is the correct answer?

Thanks!

s1lntz · Answer

Question states k and n are positive integers. N cannot be zero since zero is not a positive integer.

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IanStewart · Answer

You'll never need to worry about zero in divisibility questions on the GMAT anyway, and in this question (as in any divisibility question) the unknowns are restricted to positive integers. But in your example, you start off by positing that n is zero, but in your conclusion you seem to be instead assuming that it's k that is zero (we're asked if k is a factor of n, and you conclude by saying "since 0 is not a factor of any number", so I gather you're assuming at this point that it's k that is zero). So I think you've mixed up which number is zero in your example, and if you straighten that out, the answer will still make sense when n=0, though you won't need to worry about cases like that in any event.

J2S2019 · Answer

Both are +Ve numbers,
a is always true mate.

Tyle · Answer

For this type of question (factors), I always plug in numbers, numbers usually don't lie, unless you miss out some special case. When you plug a lot of numbers and the case don't change, then it's the answer

since n is a multiple of k, let say k=2 n=2,4,6,8,10
then 3n=6,12,18,24,30 all divisible by 2(=k)

Put k=3,4 the answer is the same

If k and n are positive integers, is k a factor of 3n

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