CAT DS question: a^2 - b^2

[dudewheysmehemail]

Hi all,

I took the first GMAT CAT exam last night and got the exam reset to take it again before I had a chance to review the answers for questions which I got wrong. DOH!
I have not been able to find it online which is why I'm posting it here.

Here is the question as best as I can piece it together from my scratch work.
Data Sufficiency:
a b and c are all integers. What is the value of (a^2) - (b^2)?
1. a = (c-1)^2
2. b = (c^2) -1

Just looking at the question I would guess that answer choice A, B, and D are wrong, since 1 doesn't mention anything about "b" and 2 doesn't mention anything about "a". So by themselves they are each not sufficient, leaving the correct answer to be either C or E.

I factored a^2 - b^2 = (a+b)(a-b) and tried to plug in the values from the statements in and got this:
(a+b)(a-b)
=( (c-1)^2 + (c^2 -1) ) ( (c-1)^2 - (c^2 -1) )
=(c^2 - 2c + 1 + c^2 - 1)(c^2 - 2c + 1 - c^2 + 1)
=(2c^2 - 2c)(2 - 2c)
=4c^2 - 4c^3 - 4c + 4c^2
=-4c^3 + 8c^2 - 4c
=-4c(c^2 - 2c + 1)
=-4c(c-1)^2

Plugging in different values for c gives different results:
c(0) = 0(-1)^2 = 0
c(1) = -4(1-1)^2 = -4 (0) = 0
c(2) = -8(1)^2 = -8

So I chose E as the answer, but I got it wrong meaning that C is the answer.

Can someone help explain how to solve this please?

Many thanks!!
--Rishi

[tim]

your work is correct. you must have either copied the question incorrectly or misread the answer..