M02-23

Question

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

(1)  n = 3 
 
(2)  x = 12

Bunuel · Accepted Answer

Official Solution:

If  x  and  n  are positive integers, is  n  a factor of  x(x+1)(x+2) ? 
 
(1)  n = 3 . 
 
The question can be rephrased as: is  x(x+1)(x+2)  divisible by 3? Given that  x(x+1)(x+2)  represents the product of three consecutive integers, one of them is inevitably divisible by 3. Therefore,  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 definitively answer the question. For instance, if  n = 1 , the answer would be YES, but if  n = 17 , the answer would be NO. Not sufficient.

Answer: A

darren1985 · Answer

I understand and thanks for the explanation.

tani24 · Answer

Cant X=0 and the consecutive numbers be 0,1 &2. The question says X is a positive integer and hence can be 0.

Bunuel · Answer

ZERO.

1. 0 is an integer.

2. 0 is an even integer. An even number is an   integer   that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.

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Hope it helps.

Aishyk97 · Answer

Hi  Bunuel .

I understand that in this question they are talking about positive integers but even if x = 0 and numbers 0*1*2 = 0
and zero is divisible by any number.
So it will be sufficient.

Is this correct?

Bunuel · Answer

Yes, the product of any three consecutive integers is divisible by 3. So, even if one of the integers is 0, the product will be 0, which is divisible by 3.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

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