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# GRE Arithmetic If x is positive and -x < y < 0

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GRE Arithmetic If x is positive and -x < y < 0 [#permalink]  30 Nov 2015, 07:44
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91% (00:38) correct 8% (00:58) wrong based on 12 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

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Ryan Born, Senior GRE Instructor, PowerScore Test Prep
Free GRE 101 Webinar, September 26 @ 8pm Eastern Time.

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Joined: 29 Sep 2015
Posts: 24
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Kudos [?]: 25 [1] , given: 0

Re: GRE Arithmetic If x is positive and -x < y < 0 [#permalink]  30 Nov 2015, 07:45
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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. $$(-1)^2 - 2^2 = 1 - 4 = -3$$

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Ryan Born, Senior GRE Instructor, PowerScore Test Prep
Free GRE 101 Webinar, September 26 @ 8pm Eastern Time.

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

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