x^3 – x^2 is a square

[Brent@GMATPrepNow]

If x is an integer, and 100≤x≤200, how many values of x exist such that x^3 – x^2 is a square?
A) 4
B) 5
C) 6
D) 7
E) 8

Please note that this is not an official GMAT question; it’s my attempt to create difficult (650+ level) GMAT-style questions for this forum.

[DanaJ]

Well, if x^3 - x^2 is a square, then x^2 (x - 1) is a square or x - 1 is a square. Since x is between 100 and 200, we have the following values for squares:
100
121
144
169
196
with corresponding +1 values. This makes for 5 solutions.

Welcome back, Brent! I have the feeling you haven;t posted much these past few days, but maybe I'm wrong... IMHO, your questions are one of the most representative for the GMAT....

[Brent@GMATPrepNow]

Nice work, Dana. The answer is 5
I've been working on other things, but will be posting more often again.
Thanks.

[awesomeusername]

It took me a bit to see that a square * a square = a square. Thus, if (x-1) is a square, then (x^2)(x-1) is a square. And like Dana said, there are 5 squares greater than or equal to 100 and less than or equal to 200.

Good question!