Consecutive integers

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williamthesituation: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Mon Jan 25, 2010 4:12 pm

by williamthesituation » Sun Feb 21, 2010 8:50 pm

If x^3 -x = p, and x is odd, is p divisible by 24

p = (x-1)x(x+1)

We have two evens and one odd, the two evens have at least three 2's as prime factors, so to make 24 we need a 3.

My question is why does X which is odd have to be a multiple of 3, why can't X be 1, and then in that case we would only have 0,1,2 sequentially...... Is there some rule that says you can't have zeros or 1's in questions like these?

The book states in any set of 3 consecutive integers, one of the integers will be a multiple of 3, what if the 3 integers were 0,1,2 or -1,0,1???

Can someone shed light into whether or not you can go into negatives on questions like these or maybe i'm missing something else all together..

Thanks.

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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Sun Feb 21, 2010 8:55 pm

williamthesituation wrote:If x^3 -x = p, and x is odd, is p divisible by 24

p = (x-1)x(x+1)

We have two evens and one odd, the two evens have at least three 2's as prime factors, so to make 24 we need a 3.

My question is why does X which is odd have to be a multiple of 3, why can't X be 1, and then in that case we would only have 0,1,2 sequentially...... Is there some rule that says you can't have zeros or 1's in questions like these?

The book states in any set of 3 consecutive integers, one of the integers will be a multiple of 3, what if the 3 integers were 0,1,2 or -1,0,1???

Can someone shed light into whether or not you can go into negatives on questions like these or maybe i'm missing something else all together..

Thanks.

My question is why does X which is odd have to be a multiple of 3, why can't X be 1, and then in that case we would only have 0,1,2 sequentially...... Is there some rule that says you can't have zeros or 1's in questions like these?
Hey williamthesituation,
in this situation,if x=1
x^3 -x = p will be 0.
Now unless otherwise given we cannot take 0 as one of the no.s,because in that case it would be senseless to give
that"p divisible by 24" because 0 is divisible by any number 0/24 =0
It could have been 25,26,90,101 in place of 24 but if you took 0 the answer would have been same.
Now,that would have been an ambiguity.

I hope you get it now why 0 can't be taken.

It takes time and effort to explain, so if my comment helped you please press Thanks button

Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

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williamthesituation: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Mon Jan 25, 2010 4:12 pm

by williamthesituation » Mon Feb 22, 2010 10:43 am

I'm not sure I follow you, so you are saying if X is 1 , then P is divisible by 24 so that would answer the question.. But that is not the intention of the question? The answer states that X is a multiple of 2 since there are three consecutive integers, I think the answer hinges on that?

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Mon Feb 22, 2010 1:55 pm

williamthesituation wrote:If x^3 -x = p, and x is odd, is p divisible by 24

p = (x-1)x(x+1)

We have two evens and one odd, the two evens have at least three 2's as prime factors, so to make 24 we need a 3.

My question is why does X which is odd have to be a multiple of 3, why can't X be 1, and then in that case we would only have 0,1,2 sequentially...... Is there some rule that says you can't have zeros or 1's in questions like these?

The book states in any set of 3 consecutive integers, one of the integers will be a multiple of 3, what if the 3 integers were 0,1,2 or -1,0,1???

Can someone shed light into whether or not you can go into negatives on questions like these or maybe i'm missing something else all together..

Thanks.

If a question doesn't put limitations on the numbers involved, then all numbers are fair game.

So, there's no reason why x couldn't be -1 or 1.

If x does equal -1 or 1, we get p=0. Since 0 is divisible by all non-0 numbers, that generates a "yes" answer to the question.

Here we know that x is odd, so x must be an integer, which is all we need to guarantee a "yes".

(By the way, I'm assuming that this is actually a data sufficiency question and that you just haven't provided both statements; otherwise, this question makes no sense at all, since there are no "yes/no" questions in problem solving. Please make sure you post the entire question in the future so we can have better discussions!)

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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