M7MBA wrote:Is x > y ?
(1) ax > ay
(2) (a²)x > (a²)y
Target question: Is x > y ?
Statement 1: ax > ay
WARNING: Some students will divide both sides by a and
incorrectly conclude that x > y.
However, before we divide by a variable, we must ensure that the variable is EITHER positive OR negative, because if we divide by a
negative value, we must reverse the direction of the inequality, and if we divide by a
positive value, the direction of the inequality stays the same. As it stands, we don't know whether a is positive or negative.
To see what I mean, consider these values of a, x and y that satisfy the given condition:
Case a: a = 1, x = 3 and y = 2, in which case
x > y
Case b: a = -1, x = 2 and y = 3, in which case
x < y
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: (a²)x > (a²)y
First of all, we can conclude that a DOES NOT equal 0, since the inequality wouldn't hold up.
This means that a² is a POSITIVE number.
So, we can safely divide both sides of the inequality by a² to get:
x > y
So, the answer to the target question is
YES, x IS greater than y
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
