Bunuel wrote:

What is the remainder when x^2 - y^2 is divided by 3?

(1) x^2 is divisible by 6. No info about y. Not sufficient.

(2) y^2 is divisible by 9. No info about y. Not sufficient.

(1)+(2) x^2 - y^2 = (multiple of 3) - (multiple of 3) = (multiple of 3), thus the remainder is zero. Sufficient.

Answer: C.

Why do we need information about y for 2)? Don't we need information about x^2 to determine the answer in (2)?

(x^2 - y^2)%3 = ((x^2)%3-(y^2)%3)%3

1) (0 - (y^2)%3)%3 = -(y^2)%3 | NS

2)((x^2)%3-0)%3 = (x^2)%3 | NS

(1)+(2): 0