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Is 2x - 3y < x^2 ? (1) 2x - 3y = -2 (2) x > 2 and y

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Manager
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Is 2x - 3y < x^2 ? (1) 2x - 3y = -2 (2) x > 2 and y [#permalink]

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New post 12 Feb 2009, 20:08
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Is \(2x - 3y < x^2\) ?

(1) \(2x - 3y = -2\)

(2) \(x > 2\) and \(y > 0\)

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Director
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Re: DS: Inequality GPREP [#permalink]

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New post 12 Feb 2009, 20:18
D.

1) x^2 is always going to be +ve

2) for given conditions the condition is always true.
(if y>0, -3*y is always negative and will subtract from 2*x, x being greater than 2, x^2 will be always greater than 2x., so LHS will always be smaller than RHS)

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Re: DS: Inequality GPREP [#permalink]

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New post 12 Feb 2009, 22:44
I too agree with alpha_plus_gamma.

Both options are independently sufficient to answer the question.
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Director
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Re: DS: Inequality GPREP [#permalink]

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New post 15 Feb 2009, 05:34
alpha_plus_gamma wrote:
D.

1) x^2 is always going to be +ve

2) for given conditions the condition is always true.
(if y>0, -3*y is always negative and will subtract from 2*x, x being greater than 2, x^2 will be always greater than 2x., so LHS will always be smaller than RHS)


Explanation for 2) is not so convincing...
2) >> For 2x-3y <x^2 , if 2x-3y is negative then the condition is always true. So we have to only concentrate on the conditions where 2x-3y can be positive. For this, we should take x as close to 2(because x>2) as possible and y as close to 0 as possible. Lets take x=2.000001 and y=0.0000001 which is approx 4-3=1 and 1>2.000001.

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Re: DS: Inequality GPREP [#permalink]

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New post 19 Mar 2009, 22:59
convert the equation 2x-3y<x^2 to y> x(2-x)/3

st. 1 is easy to say sufficient.

st-2 from above converted equation it is easy to see that y is positive as y >1 and another side is -Ve as x>2 given
hence suff.

Ans D

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Re: DS: Inequality GPREP   [#permalink] 19 Mar 2009, 22:59
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