If y ≠0, is a^x > y?
1) a = -y = |x|
2) a < 1
Target question: Is a^x > y?
Statement 1: a = -y = |x|
We're told that y ≠0, which means a ≠0 and x ≠0.
If x ≠0, we can be certain that |x| is POSITIVE, which means
a is POSITIVE and -y is POSITIVE
If -y is POSITIVE, then
y is NEGATIVE
Aside: x can be either positive of negative, but this doesn't play a role in the answer.
So, all of this means that a^x = (
some POSITIVE value)^x
Since a positive number raised to ANY EXPONENT will yield a positive result, we can conclude that
a^x must be POSITIVE.
Since we also know that
y is NEGATIVE, we can be
certain that
a^x > y
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: a < 1
Since there's no information about x or y, this statement doesn't
FEEL sufficient. So I'm going to TEST some values.
There are several set of values that satisfy statement 2. Here are two:
Case a: a = 1/2, x = 1 and y = -1, in which case
a^x > y
Case b: a = 1/2, x = 1 and y = 1, in which case
a^x < y
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Answer =
A
Cheers,
Brent
