Is 2x-3y < x^2?

[ambikasrinivas]

From GMAT Prep exam

Is 2x-3y < x^2?

(1) 2x-3y = -2
(2) x>2 and y>0

Answer D

I don’t understand how to get this answer with the statements alone. I can see how to use them together, but not alone. Thanks!

[george.kourdin]

this is what id do - if anyone has another way or see any mistakes- please reply

1) try to simplify the question stem. taking square root of both sides doesn't really get us anywhere. move on to answer choices

a) 2x-3y=-2
2x = 3y-2
plug it into the original we get 3y-2-3y<x^2
-2<x^2
sufficient ....x^2 will always be > 0 regardless of x so its AD

b) x>2 and y>0
so x is some number > 2 and y is positive
try plugging any combination of numbers x and y and x^2 will always be greater because -3 will always diminish the expression

[RonPurewal]

this is what id do - if anyone has another way or see any mistakes- please reply

1) try to simplify the question stem. taking square root of both sides doesn't really get us anywhere. move on to answer choices

a) 2x-3y=-2
2x = 3y-2
plug it into the original we get 3y-2-3y<x^2
-2<x^2
sufficient ....x^2 will always be > 0 regardless of x so its AD

i suppose this correct, but why are you messing with the equation?
the left-hand side of this choice is 2x - 3y. the left-hand side of the prompt question is *also* 2x - 3y. so, for heaven's sake, don't break up that expression.

this answer choice just tells you that 2x - 3y = -2. this can be substituted directly into the prompt question, without any algebra or rearrangement, to give "Is -2 < x^2?"
the answer is yes, because x^2 must be either 0 or positive.

b) x>2 and y>0
so x is some number > 2 and y is positive
try plugging any combination of numbers x and y and x^2 will always be greater because -3 will always diminish the expression

you can also note that, if x > 2, then 2x is already less than x^2 (because 2x is 2 times x, and x^2 is x times x; we know that x > 2, so x times x > 2 times x.)
therefore, if 2x is already less than x^2, then 2x minus some positive number (i.e., 2x - 3y) -- which is an even smaller number -- will also be less than x^2.

[abdul_tt]

Is 2x - 3y < x2 ?
(1) 2x - 3y = -2
(2) x > 2 and y > 0.

Statement 1, Ron has already explained brilliantly.

Statement 2
Rephrase,
Is x^2> 2x-3y
Is x^2 - 2x > - 3 ( y )
Is x(x-2) > -3 y

we know (x-2) is positive , x is positive, and y is positive
Therefore, l.h.s is positive and r.h.s is negative because y is positive.

Answer. D

[RonPurewal]

that rearrangement works, too, yes. that's another nice way to solve the problem.

cool!