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# If p and q are positive integers, and the remainder obtained when p is

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Senior Manager
Joined: 18 Aug 2009
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Schools: UT at Austin, Indiana State University, UC at Berkeley
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If p and q are positive integers, and the remainder obtained when p is [#permalink]

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17 Mar 2011, 00:27
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25% (medium)

Question Stats:

74% (01:31) correct 26% (01:24) wrong based on 237 sessions

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If p and q are positive integers, and the remainder obtained when p is divided by q is the same as the remainder obtained when q is divided by p, which of the following is a possible value of pq?

(A) 62
(B) 55
(C) 42
(D) 36
(E) 24
[Reveal] Spoiler: OA

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Kudos [?]: 145 [0], given: 16

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Re: If p and q are positive integers, and the remainder obtained when p is [#permalink]

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17 Mar 2011, 00:37
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I am not too sure on this. I guess it is possible only when p and q are both same. If they are both same, pq must be a perfect square.

36 is a perfect square.

Ans: "D"
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Kudos [?]: 2089 [1], given: 376

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Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
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Kudos [?]: 399 [0], given: 123

Re: If p and q are positive integers, and the remainder obtained when p is [#permalink]

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17 Mar 2011, 00:56
62=2*31
55=5*11
42=2*21=6*7=3*14
24=2*12=3*8=4*6
36=2*18=3*12=4*9=6*6
hence D

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Kudos [?]: 399 [0], given: 123

Senior Manager
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Concentration: General Management, Social Entrepreneurship
Schools: HBS '14 (A)
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Re: If p and q are positive integers, and the remainder obtained when p is [#permalink]

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17 Mar 2011, 01:18
Two numbers giving the same remainder when divided by each other should be same- and remainder zero. 36 only perfect square.

Kudos [?]: 218 [0], given: 13

Senior Manager
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Re: If p and q are positive integers, and the remainder obtained when p is [#permalink]

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23 Sep 2014, 03:25
Does anyone have an algebraic way to solve this?

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Re: If p and q are positive integers, and the remainder obtained when p is [#permalink]

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25 Jan 2016, 02:04
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If p and q are positive integers, and the remainder obtained when p is [#permalink]

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21 Mar 2016, 09:45
Hey Bunuel here is my approach
could you help with this
here => the only condition that will make the scenario possible is when the numbers are equal
hence = D
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Kudos [?]: 869 [0], given: 602

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Re: If p and q are positive integers, and the remainder obtained when p is [#permalink]

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25 May 2017, 07:34
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: If p and q are positive integers, and the remainder obtained when p is   [#permalink] 25 May 2017, 07:34
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