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

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

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

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

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.

Hope it's clear.

Thanks Bunuel.. Now it is clear

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

Here is a visual that should help.

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.

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:
\(2x-3y<2x<x^2\)
\(2x-3y<x^2\)
Thus, the answer to the question stem is YES.
SUFFICIENT.

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

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