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

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

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New post Updated on: 06 May 2015, 23:08
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Question Stats:

65% (01:49) correct 35% (01:49) wrong based on 252 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, 03:56.
Last edited by PrepTap on 06 May 2015, 23:08, edited 1 time in total.
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Re: Is n(n+1)(n+2) divisible by 24?  [#permalink]

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New post 29 Apr 2015, 04:10
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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

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

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New post 30 Apr 2015, 04:34
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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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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

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

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New post 24 Aug 2018, 19:12
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
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Re: Is n(n+1)(n+2) divisible by 24? &nbs [#permalink] 24 Aug 2018, 19:12
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Is n(n+1)(n+2) divisible by 24?

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