dinesh8 wrote:

If t is a positive integer and the 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 came up with C.

Statement 2: We know t^2 when divided by 7 gives remainder 1

e.g. 36, 64, 139 (i.e. 6^2, 8^2, 13^2)

So,

t^2 + 6 must be divisible by 7 (if you add the remainder 1 to 6)

But we do not know anything about 5t hence INSUFF.

St.1: When t is divided by the remainer is 6. INSUFF

Together,

From 1 we know t^2 + 6 gives remainder 0

From 2 we know 5t gives remainder 6

Hence the remainder for t^2 + 5t + 6 = 6

Took me close to 4 mins to get this by the way. What is the OA?