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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]

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30 Oct 2008, 16:29
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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.
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30 Oct 2008, 18:18
A
(t+3)(t+2) divided by 7 gives a reminder of 2
1. t = 7x+6 , x = 0,1,2,3,....
t = 6,13,20... etc
r comes out to be 2 - Suff

2. In Suff - r is different
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30 Oct 2008, 19:30
amitdgr wrote:
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.

1: t = 7k+6

= t^2+5t+6
= (7k+6)^2 + 5 (7k+6) + 6
= 49k^2 + 84k + 6 + 35k + 30 + 6
= 49k^2 + 119k + 72

when divided by 7, (49k^2 + 119k + 72) results in 2 as reminder. suff...

2: t^2 = 36 and 64 both result5s in reminder 1. nsf...

So A.
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31 Oct 2008, 10:21
GMAT TIGER wrote:
amitdgr wrote:
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.

1: t = 7k+6

= t^2+5t+6
= (7k+6)^2 + 5 (7k+6) + 6
= 49k^2 + 84k + 6 + 35k + 30 + 6
= 49k^2 + 119k + 72

when divided by 7, (49k^2 + 119k + 72) results in 2 as reminder. suff...

could you explain this one, pls
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