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# M02-23

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Math Expert
Joined: 02 Sep 2009
Posts: 43296

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15 Sep 2014, 23:18
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Question Stats:

78% (00:32) correct 22% (00:37) wrong based on 156 sessions

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If $$x$$ and $$n$$ are positive integers, is $$n$$ a divisor of $$x(x+1)(x+2)$$?

(1) $$n = 3$$

(2) $$x = 12$$
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 43296

Kudos [?]: 139200 [0], given: 12779

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15 Sep 2014, 23:18
Official Solution:

Statement (1) by itself is sufficient. The product of any three consecutive positive integers is divisible by 3.

Statement (2) by itself is insufficient. We do not know anything about $$n$$.

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02 Jan 2018, 18:18
I don't quite understand this question. Is it necessary to plug the variables into the equation to solve this problem?

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02 Jan 2018, 22:18
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Expert's post
darren1985 wrote:
I don't quite understand this question. Is it necessary to plug the variables into the equation to solve this problem?

If $$x$$ and $$n$$ are positive integers, is $$n$$ a divisor of $$x(x+1)(x+2)$$?

(1) $$n = 3$$. The question becomes: is $$x(x+1)(x+2)$$ divisible by 3? Now, since $$x(x+1)(x+2)$$ is the product of three consecutive integers, then one of them must be divisible by 3, so $$x(x+1)(x+2)$$ will be divisible by 3 for any integer value of x. Sufficient.

(2) $$x = 12$$. The question becomes: is $$12*13*14$$ divisible by n? Without knowing the value of n we cannot answer the question. For example, if n = 1, then the answer would be YES but if n = 17, then the answer would be NO. Not sufficient.

Hope it's clear.
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03 Jan 2018, 06:44
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Bunuel wrote:
darren1985 wrote:
I don't quite understand this question. Is it necessary to plug the variables into the equation to solve this problem?

If $$x$$ and $$n$$ are positive integers, is $$n$$ a divisor of $$x(x+1)(x+2)$$?

(1) $$n = 3$$. The question becomes: is $$x(x+1)(x+2)$$ divisible by 3? Now, since $$x(x+1)(x+2)$$ is the product of three consecutive integers, then one of them must be divisible by 3, so $$x(x+1)(x+2)$$ will be divisible by 3 for any integer value of x. Sufficient.

(2) $$x = 12$$. The question becomes: is $$12*13*14$$ divisible by n? Without knowing the value of n we cannot answer the question. For example, if n = 1, then the answer would be YES but if n = 17, then the answer would be NO. Not sufficient.

Hope it's clear.

Hi darren1985

Statement 1 represents a general rule when dealing with divisor 3 that you should know. Beside the above, you should know the variation for presenting 3 consecutive numbers . It could be:

(x-2)(x-1) x

or

(x-1) x (x+1)

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03 Jan 2018, 09:59
I understand and thanks for the explanation.

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Re: M02-23   [#permalink] 03 Jan 2018, 09:59
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# M02-23

Moderators: chetan2u, Bunuel

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