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# Is |x^2| - |y^2| = |x^2–y^2| ? (1) x > 0 (2) y < 0

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Math Expert
Joined: 02 Sep 2009
Posts: 60772
Is |x^2| - |y^2| = |x^2–y^2| ? (1) x > 0 (2) y < 0  [#permalink]

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06 Nov 2019, 02:06
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Difficulty:

55% (hard)

Question Stats:

56% (01:25) correct 44% (01:30) wrong based on 47 sessions

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Is $$|x^2| - |y^2| = |x^2–y^2|$$ ?

(1) $$x > 0$$

(2) $$y < 0$$

Are You Up For the Challenge: 700 Level Questions

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Joined: 23 Nov 2018
Posts: 246
GMAT 1: 650 Q49 V28
GPA: 4
Re: Is |x^2| - |y^2| = |x^2–y^2| ? (1) x > 0 (2) y < 0  [#permalink]

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06 Nov 2019, 05:06
1) x=2 , y=0 yes
Y=0, x=2 no

2) x=1, y=-1 yes
x=0 , y= -1 no

Both 1 and 2 together

X=1, y=-1 yes
X=1, y=-4 no

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Joined: 19 Oct 2018
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Re: Is |x^2| - |y^2| = |x^2–y^2| ? (1) x > 0 (2) y < 0  [#permalink]

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06 Nov 2019, 06:27
$$|x^2| - |y^2| = |x^2–y^2|$$
or
is |x|≥|y|?

Sign of x or y won't tell us anything about the magnitude of x or y

Clearly E

Bunuel wrote:
Is $$|x^2| - |y^2| = |x^2–y^2|$$ ?

(1) $$x > 0$$

(2) $$y < 0$$

Are You Up For the Challenge: 700 Level Questions
Manager
Joined: 10 Dec 2017
Posts: 177
Location: India
Is |x^2| - |y^2| = |x^2–y^2| ? (1) x > 0 (2) y < 0  [#permalink]

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06 Nov 2019, 07:10
Bunuel wrote:
Is $$|x^2| - |y^2| = |x^2–y^2|$$ ?

(1) $$x > 0$$

(2) $$y < 0$$

Are You Up For the Challenge: 700 Level Questions

$$Ix^2I=lxl^2=x^2$$
$$x^2-y^2=Ix^2-y^2I$$
or
$$x^2-y^2>=0$$
From 1)
Not sufficient
From 2)
Not sufficient
From 1 and 2
x=4, y= -1(yes)
x=4, y=-9(No)
E:)
Is |x^2| - |y^2| = |x^2–y^2| ? (1) x > 0 (2) y < 0   [#permalink] 06 Nov 2019, 07:10
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