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.
