vipulgoyal wrote:Is 2x^2 - 7xy - 15y^2 > 0?
(1) 2x > -3y
(2) x > 5y
This is a good candidate for rephrasing the target question. (
Aside: We have a free video on this technique:
https://www.gmatprepnow.com/module/gmat- ... cy?id=1100)
Target question:
Is 2x^2 - 7xy - 15y^2 > 0?
We can factor the expression: 2x^2 - 7xy - 15y^2 = (2x + 3y)(x - 5y). So, . . .
Rephrased target question:
Is (2x + 3y)(x - 5y) > 0?
Statement 1: 2x > -3y
Add 3y to both sides to get
2x + 3y > 0
In other words,
(2x + 3y) = some positive value, so let's plug that into our target question. We get:
Is (some positive value)(x - 5y) > 0?
Since (x - 5y) can have either a positive or negative value, (
some positive value)(x - 5y) can evaluate to be either positive or negative.
Since we cannot answer the
rephrased target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x > 5y
Subtract 5y from both sides to get
x - 5y > 0
In other words,
(x - 5y) = some positive value, so let's plug that into our target question. We get:
Is (2x + 3y)(some positive value) > 0?
Since (2x + 3y) can have either a positive or negative value, (2x + 3y)(
some positive value) can evaluate to be either positive or negative.
Since we cannot answer the
rephrased target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
Statement 1 tells us that
(2x + 3y) = some positive value
Statement 2 tells us that
(x - 5y) = some positive value
As such, it
must be true that
(2x + 3y)(x - 5y) > 0
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer =
C
Cheers,
Brent
