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# Is n(n+1)(n+2) divisible by 24?

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Manager
Joined: 22 Apr 2015
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Is n(n+1)(n+2) divisible by 24?  [#permalink]

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Updated on: 07 May 2015, 00:08
1
9
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Difficulty:

55% (hard)

Question Stats:

62% (01:19) correct 38% (01:15) wrong based on 242 sessions

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Is n(n+1)(n+2) divisible by 24?

(1) n is even
(2) (n+1) is divisible by 3 but not by 6

This question is a part of the series of original questions posted by PrepTap. Follow us to receive more questions like this.

Originally posted by PrepTap on 29 Apr 2015, 04:56.
Last edited by PrepTap on 07 May 2015, 00:08, edited 1 time in total.
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Re: Is n(n+1)(n+2) divisible by 24?  [#permalink]

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29 Apr 2015, 05:10
2
PrepTap wrote:
Is n(n+1)(n+2) divisible by 24?

(1) n is even
(2) (n+1) is divisible by 3 but not by 6

This question is a part of the series of original questions posted every weekday by PrepTap. Follow us to receive more questions like this.
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We know that $$24=2^3*3$$
So we should check if $$n(n+1)(n+2)$$ contains $$2^3$$ and $$3$$

(we should keep in mind that when $$n$$ or $$n+1$$ or $$n+2$$ equal to $$0$$, then product of all this numbers will be equal to $$0$$ and divisible by $$24$$)

1) if $$n$$ is even than $$n+2$$ contain at least $$2^2$$ and as $$n$$ is even and not zero than $$n+1$$ will be contain $$3$$. So $$n(n+1)(n+2)$$ will be always divisible on $$24$$
Sufficient

2) from this statement we can infer that $$(n+1)$$ is odd and contain $$3$$ and that $$n$$ is even and $$n * (n+2)$$ contains at least $$2^3$$. So $$n(n+1)(n+2)$$ will be always divisible on $$24$$
Sufficient

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Is n(n+1)(n+2) divisible by 24?  [#permalink]

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30 Apr 2015, 05:34
1
PrepTap wrote:
Is n(n+1)(n+2) divisible by 24?

(1) n is even
(2) (n+1) is divisible by 3 but not by 6

This question is a part of the series of original questions posted every weekday by PrepTap. Follow us to receive more questions like this.
________________________
PrepTap is a small group of young MBAs who are trying to make learning more intuitive and effective.
Please register for a demo session on our website http://www.preptap.com in order to experience our teaching methods first hand.

When n is even n(n+1)(n+2) is always divisible by 8 and 3. Hence it will be divisible by 8*3 = 24
For the explanation look at:
solving-complex-problems-using-number-line-197045.html#p1521230

Statement 1: n is even
Sufficient

Statement 2: n+1 is divisible by 3 but not by 6
-> n+1 is odd
-> n is even
Sufficient

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Re: Is n(n+1)(n+2) divisible by 24?  [#permalink]

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24 Aug 2018, 20:12
if n is even
n=2k
n(n+2)= 2k(2k+2)=4.k.(k+1)
k(K+1) must be even because 2 consecutive number
so, n(n+2) is divisible by 8
n+1 is divisible by 3
so, the first condition is divisible by 24
Re: Is n(n+1)(n+2) divisible by 24? &nbs [#permalink] 24 Aug 2018, 20:12
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