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If p and q are consecutive positive integers, is p a multiple of 3 ? [#permalink]

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13 Dec 2011, 09:51

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Difficulty:

55% (hard)

Question Stats:

48% (01:28) correct
52% (00:19) wrong based on 21 sessions

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If p and q are consecutive positive integers, is p a multiple of 3 ?

(1) \(q\) is not a multiple of 3. (2) \(q - 1\) is not a multiple of 3.

The question is easy; however, I have a doubt in relation to the number 0. Should we consider 0 a multiple of 3? I think we should because a multiple of an integer is that integer multiplied by other integer. So , if 0 is that other integer, \(3 x 0 = 0\); thereofore, 0 is a multiple of 3. In other words, 0 would be a multiple of every number.

But I don't know whether it is the reasoning of the GMAT. Or, do they consider only positive multiples? In other words, they don't consider 0 "the other integer" to create a multiple. If they think in that way, how is the answer for this question affected? For example, in statement (2), could \(q\) be 1? In that sense, \(q-1\) would be 0, and if they only consider positive multiples, \(q-1\) would not be a multiple of 3. I know that the answer to my question is not necessary to solve this problem, but I prefer to solve that doubt for future problems.

Re: If p and q are consecutive positive integers, is p a multiple of 3 ? [#permalink]

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13 Dec 2011, 10:09

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This post received KUDOS

Expert's post

Good question. 0 is a multiple of 3. Negative numbers can also be multiples of 3. The set of multiples of 3 is {...-9, -6, -3, 0, 3, 6, 9...}

Typically, questions on the GMAT specifically call out positive multiples. And by rule, questions that ask about Least Common Multiples (LCMs) refer to the least common positive multiples.

Re: If p and q are consecutive positive integers, is p a multiple of 3 ? [#permalink]

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13 Dec 2011, 10:19

bhavinp wrote:

Good question. 0 is a multiple of 3. Negative numbers can also be multiples of 3. The set of multiples of 3 is {...-9, -6, -3, 0, 3, 6, 9...}

Typically, questions on the GMAT specifically call out positive multiples. And by rule, questions that ask about Least Common Multiples (LCMs) refer to the least common positive multiples.

I hope that helps!

Thank you bhavnip!, kudos for you

So, if this question were in the real exam, I should think that 0 is a multiple of 3, right? _________________

"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

Re: If p and q are consecutive positive integers, is p a multiple of 3 ? [#permalink]

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14 Dec 2011, 11:38

Expert's post

Happy to help!

We know that p and q are consecutive positive integers. So p could be q+1 or it could be q-1

From statement 1 we know that q is not a multiple of 3. So we know that either q+1 or q-1 is a multiple of 3, since 1 of every 3 consecutive integers must be a multiple of 3. Statement 2 tells us that q-1 is not a multiple of 3, so combining this with Statement 1, we now know that q+1 is a multiple of 3. However, we still don't know if p=q+1 or if p=q-1.

So combining both statements is not sufficient. _________________

Bhavin Parikh Magoosh Test Prep

gmatclubot

Re: If p and q are consecutive positive integers, is p a multiple of 3 ?
[#permalink]
14 Dec 2011, 11:38

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