dpark 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.

Statement (1) Says that when t is divided by 7, the reminder is 6.

Say : t = 7A + 6

t^2 = 47A^2 + 84A + 36

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

5t = 35A + 30

Hence, when 5t is divided by 7, the remainder is 2.

Hence, the remainder of t^2+5t+6 is divided by 7 would be (1+2+6)/7 = 2

So, statement 1 is sufficient.

From statement 2, we cant derive what would be the value of t as t^2 can be 1 , 36, 64 ... so on. Hence, not sufficient.