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If n and k are positive integers, is n divisible by 6?

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Re: If n and k are positive integers, is n divisible by 6?  [#permalink]

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New post 02 Jan 2017, 05:34
we need to check whether or not n/6 is and integer
Lets look at statements
Statement 1
n=k(k+1)(k-1)
n=(k-1)k(k+1)
There is an interesting property which can be applied here incase you don't want to use the test cases approach

Property => PRODUCT OF N CONSECUTIVES IS ALWAYS DIVISIBLE BY N!

Hence n which is a product of 3 consecutive must be divisible by 3! i.e. it must be divisible by 6.
Bingo.That is what we needed.
hence sufficient

Statement 2
This statement provides no clue of n
hence not sufficient.

Hence A
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Re: If n and k are positive integers, is n divisible by 6?  [#permalink]

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New post 29 Jan 2017, 17:17
1
1) k,(k+1), and (k-1) are three consecutive integers, and one of them has to be divisible by 3, which means that their product is divisible by 3. Also, either k or k+1 is an even number (divisible by 2). Since k(k+1)(k-2) is divisible by 3 and divisible by 2, it is divisible by 6.
2) k-1 is a multiple of 3. This gives us no information about n whatsoever, so this statement is insufficient.

Statement 1 alone is sufficient, but statement 2 is not sufficient.
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Re: If n and k are positive integers, is n divisible by 6?  [#permalink]

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New post 15 Jun 2017, 09:01
solved this thanks to Bunuel within sec.

k(k+1)(k-1) --> (k-1) (k) (k+1) --> three consecutive integers therefore n is divisible by 6
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Re: If n and k are positive integers, is n divisible by 6?  [#permalink]

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New post 16 Sep 2018, 23:26
sabineodf wrote:
Unsure how A is sufficient (I know that's the answer but I'm hoping someone could help show me why)

For me A is insufficient because:

if n= k(k+1)(k-1)

we can get several cases, such as

k= 0
0*1*(-1) = -1 <-- not divisible by 6

k=1
1*2*0 = 0 <-- not divisible by 6

k=2
2*3*1 = 6 <--- divisible by 6

And so on. Statement 2 could supplement to my dilemma here, but since the answer is A, does anyone have a dumbed down explanation?


k cannot be 0 as k is a positive integer. And, k cannot be 1 as n is also a positive integer. Hence, k can only be >=2.
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Re: If n and k are positive integers, is n divisible by 6? &nbs [#permalink] 16 Sep 2018, 23:26

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