netcaesar 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 dividd by 7, the remainder is 6.

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

1) sufficient

let's denote a(7) - reminder of a when divided by 7

(t^2 + 5*t + 6) (7) = 36(7) + 5*6(30) + 6(7) -> enough to calculate r (actually it's equal to 2)

2) insufficient

t^2(7) = 1 -> t(7) = 1 or t(7) = -1 (or 6)

t(7) = 1 -> (t^2 + 5*t + 6) (7) = (1 + 5 + 6)(7) = 5

t(7) = 6 -> from previous example r = 2

A is the answer