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# A multiple of 0

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Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
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Kudos [?]: 433 [0], given: 109

A multiple of 0 [#permalink]  13 Dec 2011, 08:51
00:00

Difficulty:

55% (hard)

Question Stats:

44% (01:21) correct 56% (00:18) wrong based on 18 sessions
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.

Thank you!
[Reveal] Spoiler: OA

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Magoosh Co-Founder
Joined: 17 Sep 2011
Posts: 40
Schools: UC Berkeley (Haas) - Class of 2010
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Kudos [?]: 23 [2] , given: 12

Re: A multiple of 0 [#permalink]  13 Dec 2011, 09:09
2
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.

I hope that helps!
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Bhavin Parikh
Magoosh Test Prep

Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1725
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Followers: 73

Kudos [?]: 433 [0], given: 109

Re: A multiple of 0 [#permalink]  13 Dec 2011, 09:19
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?
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Magoosh Co-Founder
Joined: 17 Sep 2011
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Schools: UC Berkeley (Haas) - Class of 2010
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Kudos [?]: 23 [0], given: 12

Re: A multiple of 0 [#permalink]  13 Dec 2011, 09:41
Expert's post
No problem! And you are correct. 0 is a multiple of 3.
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Bhavin Parikh
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Kudos [?]: 143 [0], given: 2

Re: A multiple of 0 [#permalink]  14 Dec 2011, 10:11
can some body explain this with detailed explanation. I know that 2 stmnt alone are insufficient. I am unable to combine both stmnts.
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Kudos [?]: 23 [0], given: 12

Re: A multiple of 0 [#permalink]  14 Dec 2011, 10:38
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.
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Bhavin Parikh
Magoosh Test Prep

Re: A multiple of 0   [#permalink] 14 Dec 2011, 10:38
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