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GRE Prep Club Legend  Joined: 07 Jun 2014
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GRE Math Challenge #139-x^2* y < 0 [#permalink]
Expert's post 00:00

Question Stats: 57% (00:20) correct 42% (00:18) wrong based on 28 sessions
$$(x^2)(y) < 0$$

Quantity A: xy
Quantity B: 0

• Quantity A is greater.
• Quantity B is greater.
• Both Quantities are Equal
• Cannot be determined
[Reveal] Spoiler: OA

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Sandy
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Re: GRE Math Challenge #139 [#permalink]
Expert's post
sandy wrote:
$$(x^2)(y) < 0$$

Quantity A: xy
Quantity B: 0

Since x^2 is always greater than or equal to zero, and since x^2 does not equal zero (since we're told the expression (x^2)(y) is LESS THAN 0), we can be certain that x^2 is POSITIVE and y is NEGATIVE.

Of course, that x^2 is POSITIVE tells us nothing about whether x itself is positive or negative.
So, x could be positive, or x could be negative.
This brings us to two conflicting cases:

case 1: x = 1 and y = -1
Aside: notice that this satisfies the given inequality (x^2)(y) < 0
In this case we get:
Quantity A: xy = (1)(-1) = -1
Quantity B: 0
Here, quantity B is greater.

case 2: x = -1 and y = -1
Aside: notice that this satisfies the given inequality (x^2)(y) < 0
In this case we get:
Quantity A: xy = (-1)(-1) = 1
Quantity B: 0
Here, quantity A is greater.

Since we can't conclude which quantity is greater, the correct answer is
[Reveal] Spoiler:
D

Cheers,
Brent
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Re: GRE Math Challenge #139-x^2* y < 0 [#permalink]
sandy wrote:
$$(x^2)(y) < 0$$

Quantity A: xy
Quantity B: 0

• Quantity A is greater.
• Quantity B is greater.
• Both Quantities are Equal
• Cannot be determined

$$x^2$$ is positive but we don't know whether x is positive or negative. Thus we will not get any specific answer.

The best answer is D. Re: GRE Math Challenge #139-x^2* y < 0   [#permalink] 11 Aug 2018, 12:54
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