Data Sufficiency

Is 2x - 3y < x^2 ?

1) 2x - 3y = -2

2) x>2 and y>0


Answer below.











Answer is D

Now, I feel it should be B. Because B alone can sufficiently give us NO as the answer. Any help will be appreciated, I got this problem from a set provided on this very forum, and thus can't vouch for the authenticity of the answer.

Is 2x - 3y < x^2 ?

1) 2x - 3y = -2

2) x>2 and y>0

IMO:d

s1) IF 2x-3y is negative always will be less than something square.

s2) if x>2 and y>0 always true

axat wrote:Is 2x - 3y < x^2 ?

1) 2x - 3y = -2

2) x>2 and y>0


Answer below.



Answer is D

Now, I feel it should be B. Because B alone can sufficiently give us NO as the answer. Any help will be appreciated, I got this problem from a set provided on this very forum, and thus can't vouch for the authenticity of the answer.

Hi axat,

I don't know why you don't see that 1) is straightforward but here is why:

x^2 is always a non-negative number (0 or positive).

but, since 2x - 3y = -2 , 2x -3y is negative and must be always less than x^2 .
1) sufficient

2) is a little bit more involved mathematically.

Just isolate 3y and you get to answer an equivalent but simpler question:
is 3y > 2x - x^2 ?

Now, even though you're given x > 2, plug in 2, the lower bound of x, into the expression 2x - x^2 to see what will happen. Then, the result is 0.
But because the coefficient of x^2 is negative and because x^2 increases faster than 2x, the expression 2x - x^2 will become more negative and therefore smaller as x > 0 .

Since at the same time y > 0 (given in 2)), 3y > 0 as well.

Thus 3y (positive) is always greater than 2x - x^2 (negative) given the conditions in 2).

Finally, this answers the original question.
2) is also sufficient.

D) is the correct answer.


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This was a GMAT math recipe from the GMAT Chef.