Is 2x - 3y 2 and y 0

Question

Is 2x - 3y < x^2 ?

(1) 2x - 3y = -2

(2) x > 2 and y > 0

Bunuel · Accepted Answer

Is 2x-3y-2 . Sufficient. (2) x>2 and y>0 The question asks: Is 2x-3y0 ? Since x>2 , then x(x-2) is a positive number, and since y>0 , then 3y is also positive. Thus, x(x - 2) + 3y is the sum of two positive numbers and therefore positive too. Therefore, the answer to the question is x(x-2)+3y>0 ? YES. Sufficient. Answer: D.

IanStewart · Answer

From Statement 1, we know that 2x - 3y is negative, so it certainly must be less than x^2, which cannot be negative.

From Statement 2, we know that 2 < x. Multiplying by x on both sides, that means 2x < x^2. Now, if y is positive, certainly 2x - 3y < 2x, and since 2x < x^2, then 2x - 3y is definitely less than x^2.

The answer is D.

metallicafan · Answer

Thanxs Bunuel!, you rule! 
don't you ever think in writing a book about GMAT?

saxenashobhit · Answer

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

prashantbacchewar · Answer

Bunuel,

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

Bunuel · Answer

Question: "is 2x-3y rearrange --> "is 2x-x^2-3y<0 " --> and finally the question becomes "is x(x-2)+3y>0 ?". So 2x-3y0 are the same, if you prove that x(x-2)+3y>0 is true then you know that 2x-3y

prashantbacchewar · Answer

Thanks Bunuel.. Now it is clear

EMPOWERgmatRichC · Answer

Hi All,

In this DS question, you might find that 'rewriting' the question makes it easier to answer. Either way, you'll find that a combination of logic, Number Properties and TESTing VALUES will come in handy.

We're asked if 2X - 3Y < X^2. You can 'rewrite' the question to ask if 2X < X^2 + 3Y. Either way, this is a YES/NO question.

Fact 1: 2X - 3Y = -2

Here, the 'original' version of the question is probably easier to answer, since we now have a value that we can 'substitute' in for (2X - 3Y)....

The question now asks.....

Is -2 < X^2?

X^2 can be 0 or any positive value, so with ALL possible values of X, the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

Fact 2: X > 2 and Y > 0

With this Fact, the 'rewritten' version of the question is probably easier to answer.

Since we know that X > 2......2X will ALWAYS be < X^2.

We also know that Y > 0, so (X^2 + 3Y) will get larger as Y gets larger. This all serves as evidence that....

2X is ALWAYS < X^2 + 3Y. The answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

Final Answer:

Show Spoiler

D

GMAT assassins arne't born, they're made,
Rich

mcelroytutoring · Answer

Here is a visual that should help.

anairamitch1804 · Answer

This is a yes/no problem

Statement1: 
if 2x - 3y = -2 , then 2x - 3y will always be less than x^2 because x^2 has to be a positive number. Sufficient to answer the question

Statement2: 
2x=x^2 when x equals 2. This means that 2x is always less than x^2 if x is greater than 2. 3y is not a concern because we are subtracting that quantity from 2x. 3y would only be a concern if y is less than zero and the "-3y" becomes a positive term. However, statement 2 lists that y>0. This means that the term "-3y" will always be negative, and for possible combinations of x and y, 2x-3y will always be greater than x^2. Sufficient to answer the question.

Both statements are sufficient, the answer should be D.

GMATGuruNY · Answer

Statement 1: 2x - 3y = -2 Substituting 2x-3y=-2 into 2x - 3y < x^2 , we can rephrase the question stem as follows: Is -2 < x^2 ? Since the least possible value for x^2 is 0, the answer to the rephrased question stem is YES. Statement 2: x > 2 and y > 0 If x=2 , then 2x=x^2 . For all values of x greater than 2, 2x < x^2 . Since y>0, 2x-3y < 2x. Linking together 2x-3y<2x and 2x< x^2 , we get: 2x-3y<2x

BrentGMATPrepNow · Answer

Target question : Is 2x - 3y < x² ? Statement 1 : 2x - 3y = -2 The target question becomes: Is -2 < x² ? Since x² is greater than or equal to 0 for all values of x, we can be certain that -2 is less than x² Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2 : x > 2 and y > 0 Let's first take the target question, Is 2x - 3y < x²? , and subtract 2x from both sides to get: Is -3y < x² - 2x? Factor to get: Is -3y < x(x - 2)? If x > 2 then (x - 2) is POSITIVE, and x is POSITIVE Conversely, if y > 0, then -3y is NEGATIVE. The rephrased target question becomes, Is some NEGATIVE number < (POSITIVE)(POSITIVE)? The answer to the rephrased target question is YES, some NEGATIVE number is less than (POSITIVE)(POSITIVE) Since we can answer the target question with certainty, statement 2 is SUFFICIENT Answer: D Cheers, Brent

MacT750 · Answer

but cant x be imaginary number i.e 3i where3i^2=-9

Bunuel · Answer

No.  On the GMAT, all numbers are real by default.

Is 2x - 3y < x^2 ? (1) 2x - 3y = -2 (2) x > 2 and y > 0

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