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TAGS: Intern  Joined: 29 Sep 2015
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GRE Arithmetic If x is positive and -x < y < 0 [#permalink]
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Question Stats: 90% (00:35) correct 9% (00:58) wrong based on 11 sessions
If $$x$$ is positive and $$-x < y < 0$$, then which of the following must be negative?

A. $$(x + y)^2$$
B. $$(x - y)^2$$
C. $$(y - x)^2$$
D. $$x^2 - y^2$$
E. $$y^2 - x^2$$
[Reveal] Spoiler: OA

_________________

Ryan Born, Senior GRE Instructor, PowerScore Test Prep
Free GRE 101 Webinar, September 26 @ 8pm Eastern Time.
Reserve your spot! https://www.powerscore.com/freeseminars/gre/ Intern  Joined: 29 Sep 2015
Posts: 24
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Re: GRE Arithmetic If x is positive and -x < y < 0 [#permalink]
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[Reveal] Spoiler: Solution
Step 1: Rule out products of squaring. The square of any real number (meaning any value on the number line) cannot be negative. Since squaring is the final operation in (A), (B), and (C), those answer choices must work out to either zero or some positive value.

A. $$(x + y)^2$$
B. $$(x - y)^2$$
C. $$(y - x)^2$$

Step 2: Assign values to x and y if you're unsure whether $$x^2$$ or $$y^2$$ is bigger. Neither x nor y is equal to zero, so both $$x^2$$ and $$y^2$$ are positive. If $$x^2 > y^2$$, then (E) must be correct, since a smaller positive minus a larger positive must equal a negative.

Let $$x = 2$$ and $$y = -1$$.
D. $$2^2 - (-1)^2 = 4 - 1 = 3$$
E. $$(-1)^2 - 2^2 = 1 - 4 = -3$$

_________________

Ryan Born, Senior GRE Instructor, PowerScore Test Prep
Free GRE 101 Webinar, September 26 @ 8pm Eastern Time.
Reserve your spot! https://www.powerscore.com/freeseminars/gre/

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Re: GRE Arithmetic If x is positive and -x < y < 0 [#permalink]
RBornPowerScore wrote:
If $$x$$ is positive and $$-x < y < 0$$, then which of the following must be negative?

A. $$(x + y)^2$$
B. $$(x - y)^2$$
C. $$(y - x)^2$$
D. $$x^2 - y^2$$
E. $$y^2 - x^2$$

Amazing question.

Note : x is a positive number but negative x is greater than y, which is also negative. So, we can conclude that positive x is greater that the value of y.

Suppose ,

x = 10 and negative x = -10.

y = -5

Option E:

$$y^2 - x^2$$ = (-5)^2 - ( 10)^2

= 25 -100

= -75

The best answer is E. Re: GRE Arithmetic If x is positive and -x < y < 0   [#permalink] 17 Jul 2018, 15:20
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