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(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.

1. you should see you can replace the terms of 2x-3y so you get -2<x^2 ? since any number squared is positive this is SUFF 2. You can view this problem in another way: 2x will always be less than x^2 as x >2. And since y >0 that means the left side 2x-3y will be even fewer than 2x so left side will always be less than x^2 SUFF (brunnel's answer is another approach so i chose this way from another pespective) _________________

1. you should see you can replace the terms of 2x-3y so you get -2<x^2 ? since any number squared is positive this is SUFF 2. You can view this problem in another way: 2x will always be less than x^2 as x >2. And since y >0 that means the left side 2x-3y will be even fewer than 2x so left side will always be less than x^2 SUFF (brunnel's answer is another approach so i chose this way from another pespective)

Thanks shaselai, much easier to follow. _________________

1. you should see you can replace the terms of 2x-3y so you get -2<x^2 ? since any number squared is positive this is SUFF 2. You can view this problem in another way: 2x will always be less than x^2 as x >2. And since y >0 that means the left side 2x-3y will be even fewer than 2x so left side will always be less than x^2 SUFF (brunnel's answer is another approach so i chose this way from another pespective)

Thanks shaselai, much easier to follow.

Just a little correction, which makes no difference for this particular question but is very important, as GMAT likes to catch on differences like this: square of a number is non-negative (and not positive) --> x^2\geq{0}, because if x=0 then x^2=0.

In heat of solving question, I missed to notice that statement 1 is same as inquality question. I concluded with D but after spending time _________________

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Your explaination for why second statement alone is sufficient to answer the question proves that x(x-2)+3y > o. But this does not answer whether ( 2x-3y < x^2)

Your explaination for why second statement alone is sufficient to answer the question proves that x(x-2)+3y > o. But this does not answer whether ( 2x-3y < x^2)

Can you please explain.

Thanks

Question: "is 2x-3y<x^2?" --> rearrange --> "is 2x-x^2-3y<0" --> and finally the question becomes "is x(x-2)+3y>0?". So 2x-3y<x^2 and x(x-2)+3y>0 are the same, if you prove that x(x-2)+3y>0 is true then you know that 2x-3y<x^2 is also true.

Re: Is 2x - 3y < x^2 ? (1) 2x - 3y = -2 (2) x > 2 and y [#permalink]
09 Apr 2013, 09:04

Dear Bunuel Need some clarification on this question, as i am getting A as an answer What i did: 2x - 3y < X^2 - since x^2 will be positive number i divided both sides by X^2 - the equation provided became (2x-3y)/x^2<0. later when i plugged in various numbers to test the validity they gave me both a Yes and a No answer. Where am i going wrong. Can you please correct me?

(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.

Answer: D.

Great Manipulation for Statement 2! _________________

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