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
