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M02-23

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New post 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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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.

Answer: A.

Hope it's clear.
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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.

Answer: A.

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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New post 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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