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

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Manager
Joined: 22 Apr 2015
Posts: 63
Is n(n+1)(n+2) divisible by 24?  [#permalink]

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

55% (hard)

Question Stats:

66% (01:51) correct 34% (01:50) wrong based on 333 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

Director
Joined: 29 Jun 2017
Posts: 711
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
Director
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Posts: 711
Re: Is n(n+1)(n+2) divisible by 24?  [#permalink]

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27 Dec 2018, 02:36
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 by PrepTap. Follow us to receive more questions like this.

be careful

n(n+1)(n+2)
is 3 consecutive numbers, one of them must be divided by 3.
n is even , then n=2k, n+2=2(K+1)
n(n+2)=2k*2(k+1)=4k(k+1),
k and k+1 is 2 consecutive interger, one of them must be divided by 2
so 4k(k+1) must be divided by 8
so, the total expresstion is divided by 24

we can pick specific numbers and find the answer,

condition 2
n+1 is divided by 3 but not 6. this mean n+1 is odd . this mean n and n+2 is two consecutive even number, product of which are multiple of 8 as I prove above.
sufficient.

the takeaway is that
the product of 2 consecutive even numbers is divided by 8. remember how to prove this
if there are 3 consecutive numbers, one of them must be divided by 3

those concept is tested many times on gmat because it is basic
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Re: Is n(n+1)(n+2) divisible by 24?  [#permalink]

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27 Dec 2018, 04:44
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 by PrepTap. Follow us to receive more questions like this.

St 1 : n is even

Minimum value of n = 2

(n) (n+1) (n+2) in this case = 2 * 3 * 4 = 24 Yes

For higher even values of n, (n) (n+1) (n+2) is a higher multiple of 24

Definite Yes

Sufficient

St 2 : (n + 1) is a divisible by 3 but not by 6

Which means (n+1) is a odd multiple of 3

So (n + 1) is odd as 3 is odd

This implies n is even

Definite yes as seen from St 1

Sufficient

Choice D
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Re: Is n(n+1)(n+2) divisible by 24?   [#permalink] 27 Dec 2018, 04:44
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