Last Updated on May 11, 2023
GMAT OFFICIAL GUIDE DS
Solution:
We are given that u > 0 and that v > 0. We must determine whether u^v is greater than v^u.
Statement One Alone:
u = 1
If u = 1, then u^v = 1^v = 1 (recall that 1 raised to any power is 1) and v^u = v^1 = v (recall that any number raised to the 1st power is itself). However, since we do not know the value of v, we cannot determine whether u^v is greater than v^u.
For example, if v = 2, then u^v < v^u (1^2 < 2^1). However, if v = ½, then u^v > v^u because 1^(1/2) > (1/2)^1. Statement one is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
v > 2
Although we know that v > 2, since we do not have any information about u, we cannot answer the question. Statement two alone is not sufficient. We can eliminate answer choice B.
Statements One and Two Together:
Using statements one and two, we know that u = 1 and that v > 2. Thus, we see that:
u^v = 1^v = 1 and v^u > 2^1 (since v > 2). Since v^u > 2 and u^v = 1, v^u is greater than u^v.
Answer: C
