Does xy = 1?

[BTGModeratorVI]

Does xy = 1?

(1) x > y
(2) x = 1/y

Source: Official GMATPrep test
Answer: B

[Brent@GMATPrepNow]

Does xy = 1?

(1) x > y
(2) x = 1/y

Source: Official GMATPrep test
Answer: B

Target question: Does xy = 1?

Statement 1: x > y
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 2 and y = 0.5. In this case, xy = (2)(0.5) = 1. So, the answer to the target question is YES, xy equals 1
Case b: x = 2 and y = 1. In this case, xy = (2)(1) = 2. So, the answer to the target question is NO, xy does NOT equal 1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of testing values when a statement doesn't feel sufficient, read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: x = 1/y
Multiply both sides of the equation by y to get: xy = 1
So, the answer to the target question is YES, xy equals 1
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

ASIDE: Some students may be concerned that I just multiplied both sides of the equation by a variable (y), which opens up the potential of inadvertently multiplying by zero.
However, the equation x = 1/y implies that why cannot equal zero, because 1/0 is undefined (i.e., it cannot be evaluated to be a real number).
So, if 1/0 it's not a real number, then we cannot say that x = 1/0, since that would mean that X is also not a real number

Answer: B

Cheers,
Brent