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Gmat Prep Test 2 DS Remainder problem

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Gmat Prep Test 2 DS Remainder problem [#permalink] New post 29 Jul 2006, 23:50
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A
B
C
D
E

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Hi guys I was able to answer this question using trial and error. Was hoping you guys can give me a more mathematical way of arriving at the answer thanks.

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

I broke down the given polynomial in the question stem to arrive at
(t+3)(t+2) . So from number 1 we can tell that t+1 is divisible by 7 then I proceeded to use different values . I'm sure you guys can come up with a better way to solve this.

The answer to the question is A by the way
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Re: Gmat Prep Test 2 DS Remainder problem [#permalink] New post 30 Jul 2006, 00:17
apollo168 wrote:
Hi guys I was able to answer this question using trial and error. Was hoping you guys can give me a more mathematical way of arriving at the answer thanks.

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

I broke down the given polynomial in the question stem to arrive at
(t+3)(t+2) . So from number 1 we can tell that t+1 is divisible by 7 then I proceeded to use different values . I'm sure you guys can come up with a better way to solve this.

The answer to the question is A by the way


Given
(t+3)(t+2) = 7*q+r
S1. t = 7m+6
subsitute t
(7m+6+3)(7m+6+2) = (7m+9)(7m+8) => 72/7 r=2 : sufficient
S2. t^2 = 7n+1
t^2-1 = 7n
(t+1)*(t-1) = 7n tells that either t+1 or t-1 is multiple of 7
1. t=7k+1 or 2. t=7k-1
subsitute t
1. (7k+1+3)(7k+1+2)=(7k+4)(7k+3) => 12/7 r=5
2. (7k-1+3)(7k-1+2) = (7k+2)(7k+1) => 2/7 r=2
1!=2
thus insufficient

A it is.
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 [#permalink] New post 30 Jul 2006, 00:25
Hi from this part:
7m+6+3)(7m+6+2) = (7m+9)(7m+8) => 72/7 r=2 : sufficient

How did you arrive at 72/7?

Thanks
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 [#permalink] New post 30 Jul 2006, 00:27
apollo168 wrote:
Hi from this part:
7m+6+3)(7m+6+2) = (7m+9)(7m+8) => 72/7 r=2 : sufficient

How did you arrive at 72/7?

Thanks


(7m+9)(7m+8) = 7*7m^2+9*7m+8*7m+8*9
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 [#permalink] New post 30 Jul 2006, 00:30
Wow I get it thanks you guys are awesome!
  [#permalink] 30 Jul 2006, 00:30
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