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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 09 Nov 2015, 09:55
chetan2u wrote:
arhumsid wrote:
Bunuel wrote:

0 is divisible by every integer (except 0 itself).


Hi Bunuel

I just realized something while solving this question, please let me know if im correct on this one:

Product of n consecutive integers is always divisible by
-all integers between 1 and n inclusive.
-n!
-all the factors of n!


Can we make this generalization??


hi ,
if you mean first n consecutive integers..
then product of n consecutive integers is nothing but n! itself...


Nope i dont mean that.. I mean 'ANY n consecutive Integers'. What do you say about that?
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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?  [#permalink]

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New post 22 May 2019, 18:39
If n is divisible by 6. Shouldn't the correct answer include divisibility by both 2 and 3? Both solutions are divisible by 3 but don't imply divisibility by 2 so why isn't the answer E?
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Re: If n and k are positive integers, is n divisible by 6?   [#permalink] 22 May 2019, 18:39

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