GRE Sample Test 5 Quantitative Reasoning 2

Since a is an integer, the greatest possible value for a is 12, since 122 = 144 (note that 13 is too large since 132 = 169). The least possible value for a is –12, since (–12)2 = 144 (note that –13 is too small since (–13)2 = 169.
We can express a’s range as: –12 ≤ a ≤ 12. In this range, there are 12 negative integers (–12 thru –1), 12 positive integers (1–12), and zero.
Therefore, there are 25 possible values for a.