topspin360 wrote:Hello,
Is it true that x - z > y - z ?
(1) xz > yz
(2) x + z > y + z
Target question: Is x - z > y - z ?
This is a great candidate for rephrasing the target question (more on this important strategy in this free video:
https://www.gmatprepnow.com/module/gmat- ... cy?id=1100)
Take x - z > y - z, and add z to both sides to get z > y. So . . .
REPHRASED target question: Is x > y?
Statement 1: xz > yz
Since we don't know whether z is positive or negative, we must consider these two cases:
case a: z is positive. So, if we divide both sides by z, we get
x > y
case b: z is negative. So, if we divide both sides by z, we get
x < y
Since we can't answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Alternatively, we can show that statement 1 is not sufficient by testing possible scenarios that meet the condition that xz > yz .
case a: x = 3, y = 2, and z = 1, in which case
x > y
case b: x = 2, y = 3, and z = -1, in which case
x < y
Since we can't answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x + z > y + z
Subtract z from both sides to get
x > y
Since we can answer the
REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer =
B
Cheers,
Brent
