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vipulgoyal
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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)vipulgoyal wrote:Is 2x^2 - 7xy - 15y^2 > 0?
(1) 2x > -3y
(2) x > 5y
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
