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# For the positive integers q, r, s, and t, the remainder when

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Joined: 06 Jun 2012
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Kudos [?]: 1 [1] , given: 1

For the positive integers q, r, s, and t, the remainder when [#permalink]  21 Jul 2012, 13:38
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Question Stats:

57% (01:51) correct 42% (00:31) wrong based on 4 sessions
For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT:

A. 32
B. 38
C. 44
D. 52
E. 63
[Reveal] Spoiler: OA

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Kudos [?]: 799 [0], given: 514

Re: For the positive integers q, r, s, and t the remainder when [#permalink]  21 Jul 2012, 14:09
For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT:

1)32
2)38
3)44
4)52
5)63

Its obvious from the prompt that r is greater than 7 and t is greater than 3
so the product of rt must have at least 2 factors, one which is greater than 7 and other greater than 3
Now lets break down the possible factors so that this condition is validated
The (r,t) pairs for the options can be:
for 32, (8,4)
for 44, (11,4)
for 52 (13,4)
for 63 (9,7)
however 32 can only be written as 38*1 or 19*2 none of which can validate the prompt.
Hope this helps
Cheers
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Joined: 06 Jun 2012
Posts: 14
Concentration: Technology, Entrepreneurship
GMAT 1: Q V
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Kudos [?]: 1 [0], given: 1

Re: For the positive integers q, r, s, and t the remainder when [#permalink]  24 Jul 2012, 12:56
Thanks alot.
I figured it out after I sent the post
Just goes to show you that sleep is important.
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Try to make my way to San Jose.

??? class of 2014

MBA Section Director
Joined: 19 Mar 2012
Posts: 1273
Location: India
GPA: 3.8
WE: Marketing (Energy and Utilities)
Followers: 217

Kudos [?]: 799 [0], given: 514

Re: For the positive integers q, r, s, and t, the remainder when [#permalink]  24 Jul 2012, 12:59
no problem
i face similar fatigue in RCs
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Re: For the positive integers q, r, s, and t, the remainder when   [#permalink] 24 Jul 2012, 12:59
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