arjtryarjtry wrote:

where did i go wrong???

A. Tough one.

(1) Sufficient

t = 7k+6, where k is an integer

(7k+6)^2 + 5(7k+6) + 6

= 49k^2 +84k + 36 + 35k + 30 + 6

= 49k^2 + 119k + 72

49k^2 is divisible by 7.

119k is divisible by 7.

Thus, remainder is always remainder of 72/7, or 2.

(2) Insufficient

t^2 = 7k+1

t = +/-sqrt(7k+1) = an integer

t could be 6, 9, 15 etc...

If t = 6

t^2 + 5t + 6 = 36 + 30 + 6 = 72

72/7 = 10 R 2

If t = 15

t^2 + 5t + 6 = 225 + 75 + 6 = 306

306/9 = 34