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# If t is a positive integer and r is the remainder when t^2 +

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Senior Manager
Joined: 19 Mar 2008
Posts: 344
If t is a positive integer and r is the remainder when t^2 +  [#permalink]

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16 Aug 2008, 08:06
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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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Re: DS when divided by 7  [#permalink]

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16 Aug 2008, 10:18
judokan 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.

t^2 + 5t + 6 = (t+3)(t+2) ---- Equation 1

(1) Given: t = 7k + 6
Substitute in Eq-1
=> (7k+9)(7k+8)
=> 49k^2 + 56k + 63k + 72

Every term is divisible by 7 except 72, which when divided by 7 yields a remainder of 2
So, r = 2. SUFF

(2) t^2 = 7k + 1
List squares: 1, 4, 9, 16, 25, 36, 49, 64

Conditions is satisfied for t=6 and t=8. INSUFF

So, vote for A
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Re: DS when divided by 7  [#permalink]

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16 Aug 2008, 18:11
judokan 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.

t^2 + 5t + 6 = (t+3)(t+2)

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

t= 7k+6

(t+3)(t+2) = (7k+6+3)(7k+6+2) = (7k+7+2)(7k+7+1)
say 7k+7= x( which is alwasy divisible by 7)
(7k+7+2)(7k+7+1)= (x+2)(x+1) = x^2+3x+2 (x^2, 3x ARE DIVISIBLE 7 ..so remainder 2 )

(2) when t^2 is divided by 7, the remainder is 1
t^2 = 7m+1

t^2 + 5t + 6 = 7m+1+5t+6 = (7m+7)+5t (here first part 7m+7 alwasy divisble by 7 but we MAY have multive values for 5t
e.g say m=0 t^2 = 7m+1= 1 --> t=1 remainder 5
e.g say m=5 t^2 = 7m+1= 36 --> t=6 remainder 3

Multiple solutions
Insuffcient

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Re: DS when divided by 7 &nbs [#permalink] 16 Aug 2008, 18:11
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