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# Is |x| = |y|? (1) x = -y (2) x^2 = y^2

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Is |x| = |y|? (1) x = -y (2) x^2 = y^2  [#permalink]

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Updated on: 11 Nov 2017, 01:25
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Difficulty:

5% (low)

Question Stats:

79% (00:38) correct 21% (00:39) wrong based on 245 sessions

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Is |x| = |y|?

(1) x = -y
(2) x^2 = y^2

I found this question in GMAT Prep and selected ST2 as the answer but that's wrong.

Normally, x^2 would equal to lxl since it will contain both signs "positive as well as negative". How come st 1 is true?

Does it assume that since +x = -y, it must be true that -x is also equal to -y or?

What am I missing?

Originally posted by HarveyKlaus on 16 Dec 2015, 07:06.
Last edited by Bunuel on 11 Nov 2017, 01:25, edited 3 times in total.
Formatted the question.
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Re: Is |x| = |y|? (1) x = -y (2) x^2 = y^2  [#permalink]

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10 Nov 2017, 17:20
10
You are asked whether |x|=|y| or in other words, is the distance of x from 0 = distance of y from 0 ? You would get a yes if x= y or x=-y. Lets evaluate the choices.

Per statement 1:x=−yx=−y . Clearly this is one of the conditions we are looking for. Assume 2-3 different values. x=2, y = -2 --> 2 and -2 are both 2 units from 0 . Similar for 3/-3 or 10/-10 etc. Thus this statement is sufficient.

Per statement 2: x2=y2x2=y2 ---> x=±yx=±y. Again both the cases, x=y and x=-y give you a "yes" for the question asked as is hence sufficient.

Both statements are sufficient ---> D is the correct answer.
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Re: Is |x| = |y|? (1) x = -y (2) x^2 = y^2  [#permalink]

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16 Dec 2015, 07:38
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HarveyKlaus wrote:
Is lxl = lyl ?

A) x=-y
b) x^2 = y^2

I found this question in GMAT Prep and selected ST2 as the answer but that's wrong.

Normally, x^2 would equal to lxl since it will contain both signs "positive as well as negative". How come st 1 is true?

Does it assume that since +x = -y, it must be true that -x is also equal to -y or?

What am I missing?

You are asked whether |x|=|y| or in other words, is the distance of x from 0 = distance of y from 0 ? You would get a yes if x= y or x=-y. Lets evaluate the choices.

Per statement 1:$$x=-y$$ . Clearly this is one of the conditions we are looking for. Assume 2-3 different values. x=2, y = -2 --> 2 and -2 are both 2 units from 0 . Similar for 3/-3 or 10/-10 etc. Thus this statement is sufficient.

Per statement 2: $$x^2=y^2$$ ---> $$x= \pm y$$. Again both the cases, x=y and x=-y give you a "yes" for the question asked as is hence sufficient.

Both statements are sufficient ---> D is the correct answer.
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Re: Is |x| = |y|? (1) x = -y (2) x^2 = y^2  [#permalink]

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17 Dec 2015, 06:54
statement 1 is sufficient as absolute value for -ve should give +ve
statement 2 is sufficient as
it will give either x and y both are +ve or both are -ve
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Re: Is |x| = |y|? (1) x = -y (2) x^2 = y^2  [#permalink]

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09 Mar 2018, 03:18
HarveyKlaus wrote:
Is |x| = |y|?

(1) x = -y
(2) x^2 = y^2

I found this question in GMAT Prep and selected ST2 as the answer but that's wrong.

Normally, x^2 would equal to lxl since it will contain both signs "positive as well as negative". How come st 1 is true?

Does it assume that since +x = -y, it must be true that -x is also equal to -y or?

What am I missing?

Question:

Is |x| = |y|?

This can be represented in few ways as follow:

1. x = y

2. x = -y

3. -x = y

4. -x = -y

5. x^2 = y^2

If we can have any of these conditions, answer will be YES.

St 1: x = -y (Second condition) Sufficient

St 2: x^2 = y^2 (Fifth condition) Sufficient

(D)
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Re: Is |x| = |y| ? (1) x = –y (2) x^2 = y^2  [#permalink]

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25 Aug 2018, 10:33
dabaobao wrote:
Is |x| = |y| ?

(1) x = –y
(2) x^2 = y^2
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Is |x| = |y| ? (1) x = –y (2) x^2 = y^2  [#permalink]

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25 Aug 2018, 10:35
dabaobao wrote:
Is |x| = |y| ?

(1) x = –y
(2) x^2 = y^2

Question stem:- Is |x| = |y| ?

St1:- x = –y or, y=-x

1) if y>0 , then x<0 So, |x|=-x and |y|=y=-x implies that |x|=|y|
2) if y<0, then x>0 So, |x|=x and |y|=-y=x implies that |x|=|y|
Sufficient.

St2:-$$x^2 = y^2$$
Or, $$x^2-y^2=0$$
Or, (x+y)(x-y)=0
So, x+y=0 or x-y=0
x=-y Or, x=y
1) When x=-y ,as explained in st1(same as st1) |x|=|y|
2) When x=y or, when both x and y are equal in magnitude and posses same polarity, a) |x|=x=|y|=y (x,y>0) b)|x|=-x=|y|=-y (x,y<0)
Sufficient.

Ans. (D)
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Re: Is |x| = |y|? (1) x = -y (2) x^2 = y^2  [#permalink]

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26 Aug 2018, 02:51
dabaobao wrote:
Is |x| = |y| ?

(1) x = –y
(2) x^2 = y^2

Merging topics. Please check previous discussion.
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Re: Is |x| = |y|? (1) x = -y (2) x^2 = y^2   [#permalink] 26 Aug 2018, 02:51
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