Last Updated on May 12, 2023
GMAT OFFICIAL GUIDE DS
Solution:
We need to determine the value of x, given that x^3 < x^2.
Statement One Alone:
–2 < x < 2
We see that x could be, for example, -1 or -½.
For either of these values, we have x^3 < x^2, since x^3 will be negative and x^2 will be positive. Since we don’t have a unique value for x, statement one alone is not sufficient.
Statement Two Alone:
x is an integer greater than –2.
We see that if x = -1, then x^3 < x^2, since x^3 = -1 and x^2 = 1. If x = 0, then x^3 = x^2, since x^3 = 0 and x^2 = 0 (so x can’t be 0). Similarly, if x = 1, then x^3 = x^2, since x^3 = 1 and x^2 = 1 (so x can’t be 1). If x is an integer > 1, then x^3 will always be greater than x^2. Thus, x can’t be any integer > 1.
Therefore, we see that the only value x can be is -1. Since we have a unique value for x, statement two alone is sufficient.
Answer: B
