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If t is a positive integer and r is the remainder when

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If t is a positive integer and r is the remainder when [#permalink] New post 23 Jun 2008, 05:33
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Hi everyone,

Could you please explain the below question? Thanks in advance!

If t is a positive integer and r is the remainder when t^2 + 5t + 6 is divided by 7, what is the value of r?

(1) when t is divided by 7, the remainder is 6
(2) when t^2 is divided by 7, the remainder is 1
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Re: GMATprep - DS: remainder [#permalink] New post 23 Jun 2008, 05:48
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Answer is (A) :

(1) If the reminder of t by 7 is 6, then the reminder of t^2 by 7 is the reminder of 6^2 by 7 i.e. 1

Then the reminder of t^2+5t+6 by 7 is the reminder of 6^2+5*6+6 by 7 which is equal to 2.

==> (1) is sufficient

(2) - try for t=6 (6^2=36 : reminder is 1 when divided by 7) and you'll find a reminder of 2
- try for t=8 (8^2=64 : reminder is 1 when divided by 7) and you'll find a reminder of 5

==> (2) is insufficient
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Re: GMATprep - DS: remainder [#permalink] New post 23 Jun 2008, 05:50
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If t is a positive integer and r is the remainder when t^2 + 5t + 6 is divided by 7, what is the value of r?

(1) when t is divided by 7, the remainder is 6
(2) when t^2 is divided by 7, the remainder is 1


St1: t=7k+6 after we replace this in the equation we get 49k^2+84K+36+35k+30+6 ----suffic

St2: I am unable to make that suffic

So I go with A

What is OA?
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Re: GMATprep - DS: remainder [#permalink] New post 23 Jun 2008, 05:57
Cool thanks!!! +1 :)

Answer is indeed A. Thanks a lot Oski and iamcartic!
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Re: GMATprep - DS: remainder [#permalink] New post 23 Jun 2008, 06:02
Exactly why picking up numbers is not a proof and can lead to the wrong answers when not used properly.

Try t=8 and you'll see that the reminder by 7 is 5 and not 2.

Edit: argh, and you erased your post and make me you like an idiot ;)
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Re: GMATprep - DS: remainder [#permalink] New post 23 Jun 2008, 06:28
thanks for ur answer.... oski...

after knowing that i was wrong on picking the numbers wrongly, i felt that there was no point in keeping the post...
Re: GMATprep - DS: remainder   [#permalink] 23 Jun 2008, 06:28
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