msurls wrote:

I am struggling on this one. I understand that Statement 1 and Statement 2 are Not Sufficient. But I am not sure how to combine them algebraically and solve for statement 1 and statement 2 together. Can someone please show how to do this or an easier way to solve this?

Thanks,

Is |a^2 - b^2| < 10?(1) |a - b| < 5.

If a = b = 0, then the answer to the question is YES.

If a = 4 and b = 0, then the answer to the question is NO.

Not sufficient.

(2) |a + b| < 2

If a = b = 0, then the answer to the question is YES.

If a = 10 and b = -9, then the answer to the question is NO.

Not sufficient.

(1)+(2) Notice that |xy| = |x|*|y|, so the question asks whether |a^2 - b^2| = |(a - b)(a + b)| = |a - b|*|a + b| is less than 10. From (1) we have that 0 <= |a - b| < 5 and From (2) we have that 0 <= |a + b| < 2. Their product will be less than 10: 0 <= |a - b|*|a + b| < 10. Sufficient.

Answer: C.

Hope it's clear.