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If t is a positive integer

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If t is a positive integer

by ektamatta » Mon Jun 30, 2008 2:33 pm
If t is a positive integer and r is the remainder when t^2+5t+6 is divided by7, what is the value of r?

1. When t divided by 7, the remainder is 6

2. When t^2 divided by 7, the remainder is 1


Please explain

OA IS A
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by atlantic » Tue Jul 01, 2008 1:31 am
Hi ektamatta,

It took me almost 5 minutes. I'm sure there is a faster way.

(1) says that t/7=n6, being n a integer

t=42n, or t is multiple of 42.

Pick 42 and 84 as t, replace it on the expression and you'll find R=6 for both

(2) says that t^2/7=n

t^2=7n or t^2 is a multiple of 7

Pick 7 and 14 as t^2, replace it and you'll find R=4 and R=3

So if you manage to make all the calculations without any mistake you'll get A.
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by ildude02 » Tue Jul 01, 2008 3:23 pm
Hi Atlantic, we cannot say that "t/7 = n6", but we can say, "t= 7a + 6" where a can be any integer. But in anycase, once we say t = 7a + 6, we can substitute the value of t in the question, we will get 49a^2 + 56a + 63a + 72. We can see from it, that all numbers associated with "a" are divisble by 7 leaving 72/7. we get a remainder of 2.
atlantic wrote:Hi ektamatta,

It took me almost 5 minutes. I'm sure there is a faster way.

(1) says that t/7=n6, being n a integer

t=42n, or t is multiple of 42.

Pick 42 and 84 as t, replace it on the expression and you'll find R=6 for both

(2) says that t^2/7=n

t^2=7n or t^2 is a multiple of 7

Pick 7 and 14 as t^2, replace it and you'll find R=4 and R=3

So if you manage to make all the calculations without any mistake you'll get A.
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by gauravkhare » Thu Jul 03, 2008 11:23 am
better explanation is: the expression can be written as (t+2)(t+3), now it is given that t gives remainder of 6 , hence t+1 is a multiple. so t+2 will give 1 as remainder and t+3 will give 2 as remainder and hence we can find the value of remainder by just using info of statement 1. Statement 2 ofcourse is useless
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