Data Sufficiency

Newaz111 wrote:
If xy ≠ 0, is x/y = 1?
(1) x² = y²
(2) xy > 0

Thank You...

Target question: Is x/y = 1?

Statement 1: x² = y²
When the GMAT presents you with an equation with a squared term, they're often testing your ability to recognize that positive AND negative values often satisfy the equation. For example, the equation x² = 9 has TWO solutions: x = 3 and x = -3

There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 1 and y = 1 (notice that this meets the condition that x² = y²). In this case x/y = 1/1 = 1
Case b: x = -1 and y = 1 (notice that this meets the condition that x² = y²). In this case x/y = -1/1 = -1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: xy > 0
Case a: x = 1 and y = 1. In this case x/y = 1/1 = 1
Case b: x = 1 and y = 2. In this case x/y = 1/2
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x² = y². This tells us that x and y have the same MAGNITUDE. That is, their distances from zero on the number line are equal.
Statement 2 tells us that xy is POSITIVE. This tells us that either x and y are both positive or x and y are both negative.
If x and y are both positive AND they have the same magnitude, then x = y, which mean x/y = 1
If x and y are both negative AND they have the same magnitude, then x = y, which mean x/y = 1
So, in both possible cases, x/y = 1. So, we can be certain that x/y = 1
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent