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# Is 2x - 3y < x^2?

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Manager
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Is 2x - 3y < x^2? [#permalink]  04 Jun 2006, 00:00
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Difficulty:

65% (hard)

Question Stats:

61% (01:58) correct 39% (01:01) wrong based on 90 sessions
Is 2x - 3y < x^2?

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-2x-3y-x-100596.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 21 Oct 2014, 06:28, edited 2 times in total.
Edited the question and added the OA
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Manager
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Re: Is 2x - 3y < x^2? [#permalink]  04 Jun 2006, 02:27
dinesh8 wrote:
Is 2x-3y<x^2?

1. 2x-3y =-2
2. X> 2 and y>0

D

Statement 1
any square value is >= 0 hence x^2 > 2x-3y

Statement2

for x>2 , X^2 >2x, 2x-x^2<0
for y>0, 3y >0

therefore 3y>2x-x^2
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Re: Is 2x - 3y < x^2? [#permalink]  11 Jun 2006, 08:32
got D, although did it more by plugging in values.
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Re: Is 2x - 3y < x^2? [#permalink]  13 Jun 2006, 00:28
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Will go with D .

1) 2x-3y = -2
A square of any number is > 0 hence 2x-3y<x^2

2) x> 2 and y > 0
Putting any values for x and y and you will see that 2x-3y < x^2
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Re: Is 2x - 3y < x^2? [#permalink]  04 Jul 2013, 00:33
dinesh8 wrote:
Is $$2x-3y$$<$$x^2$$?

1. $$2x-3y =-2$$
2. $$x> 2$$ and $$y>0$$

How is it D?

I'm getting A

But in choice B there can be multiple cases

for example

X=3 and y=10 in this case its a Yes

but if x=3, y=1

the question becomes is $$X^2 > 3$$ we can't answer that?
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Re: Is 2x - 3y < x^2? [#permalink]  04 Jul 2013, 00:38
Expert's post
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fozzzy wrote:
dinesh8 wrote:
Is $$2x-3y$$<$$x^2$$?

1. $$2x-3y =-2$$
2. $$x> 2$$ and $$y>0$$

How is it D?

I'm getting A

But in choice B there can be multiple cases

for example

X=3 and y=10 in this case its a Yes

but if x=3, y=1

the question becomes is $$X^2 > 3$$ we can't answer that?

Is $$2x-3y<x^2$$?

(1) $$2x-3y=-2$$ --> question becomes: is $$-2<x^2$$? as square of a number is always non-negative ($$x^2\geq{0}$$) then $$x^2\geq{0}>-2$$. Sufficient.

(2) $$x>2$$ and $$y>0$$ --> is $$2x-3y<x^2$$ --> is $$x(x-2)+3y>0$$ --> as $$x>2$$ then $$x(x-2)$$ is a positive number and as $$y>0$$ then $$3y$$ is also a positive number --> sum of two positive numbers is more than zero, hence $$x(x-2)+3y>0$$ is true. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-2x-3y-x-100596.html
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Re: Is 2x - 3y < x^2? [#permalink]  04 Jul 2013, 00:42
Expert's post
fozzzy wrote:
dinesh8 wrote:
Is $$2x-3y$$<$$x^2$$?

1. $$2x-3y =-2$$
2. $$x> 2$$ and $$y>0$$

How is it D?

I'm getting A

But in choice B there can be multiple cases

for example

X=3 and y=10 in this case its a Yes

but if x=3, y=1

the question becomes is $$X^2 > 3$$ we can't answer that?

If x=3 and y=1 we still have an YES answer: 2*3-3*1=3<9=x^2.
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Re: Is 2x - 3y < x^2?   [#permalink] 04 Jul 2013, 00:42
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