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Is |x|>|y|?

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Is |x|>|y|?  [#permalink]

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New post Updated on: 22 Sep 2019, 23:28
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Hi,
I am reviewing the questions from the Official Practice Test 1. Can anybody help me understand question 3? (data sufficiency)

Is |x|>|y|?

(1) \(x^2>y^2\)
(2) x>y

Thank you!

Originally posted by cvargas92 on 22 Sep 2019, 15:34.
Last edited by Bunuel on 22 Sep 2019, 23:28, edited 1 time in total.
Edited the OA.
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Re: Is |x|>|y|?  [#permalink]

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New post 22 Sep 2019, 16:48
I'm unsure why statement 1 is insufficient
Absolute value determines how far a number is from zero on the number line. Squaring ensures both numbers are on the same side of zero (the positive side). This shouldn't be affected by 0<a<1, fractions, negatives etc
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Re: Is |x|>|y|?  [#permalink]

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New post 22 Sep 2019, 18:13
philipssonicare wrote:
I'm unsure why statement 1 is insufficient
Absolute value determines how far a number is from zero on the number line. Squaring ensures both numbers are on the same side of zero (the positive side). This shouldn't be affected by 0<a<1, fractions, negatives etc


because x and y, depending whether they lie between (0, 1) or (1 , inf) change the answer.
The statement is not sufficient.
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Re: Is |x|>|y|?  [#permalink]

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New post 22 Sep 2019, 18:19
cvargas92 wrote:
Hi,
I am reviewing the questions from the Official Practice Test 1. Can anybody help me understand question 3? (data sufficiency)

Is |x|>|y|?

(1) \(x^2>y^2\)
(2) x>y

Thank you!


I usually draw number line and divide it into 4 parts. (-Inf, -1][-1, 0],[0,1],[1, Inf)
Whenever you see squares, absolutes and inequalities like these, you need to make sure you don't forget testing the statements in any one of those parts.

1.
Statement 1 works for (x = 10, y = 5) and also for (x = .5, y = .10 ).
In first |x| > |y| but not so in 2nd
Hence it's NS

2.
Statement works for (x = 5, y = 2) and also for (x = -2, y = -5) .
So it's NS

If you combine them, then it can only work when
x and y are both positive and greater than 1. Then the combined statement is enough to answer the question.
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Re: Is |x|>|y|?  [#permalink]

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New post 22 Sep 2019, 22:47
navderm wrote:
philipssonicare wrote:
I'm unsure why statement 1 is insufficient
Absolute value determines how far a number is from zero on the number line. Squaring ensures both numbers are on the same side of zero (the positive side). This shouldn't be affected by 0<a<1, fractions, negatives etc


because x and y, depending whether they lie between (0, 1) or (1 , inf) change the answer.
The statement is not sufficient.


This doesn't explain anything.
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Re: Is |x|>|y|?  [#permalink]

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New post 22 Sep 2019, 23:27
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New post 22 Sep 2019, 23:27
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Re: Is |x|>|y|?   [#permalink] 22 Sep 2019, 23:27
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