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# What is the value of |x - y|?

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Math Expert
Joined: 02 Sep 2009
Posts: 50619
What is the value of |x - y|?  [#permalink]

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09 Oct 2017, 23:55
00:00

Difficulty:

45% (medium)

Question Stats:

57% (01:44) correct 43% (01:16) wrong based on 44 sessions

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What is the value of |x - y|?

(1) $$–2xy – y^2 = x^2 – 4xy – 1$$

(2) $$x^2 – x = xy$$

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Joined: 09 Jul 2017
Posts: 28
Re: What is the value of |x - y|?  [#permalink]

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10 Oct 2017, 00:55
1
IMO it's A.

Statement 1: rearrange to get the value of (x-y)^2 = 1.
Thus, |x-y|= 1.
Sufficient.

Statement 2: rearranging gives:-x(x-y-1) =0.
So, either x= 0. Thus, |x-y| = |y|. No definite value.
Or (x-y-1) = 0.
x-y = 1. |x-y| = 1.
Since, this statement gives multiple possibilities, its Not sufficient.

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Joined: 15 Aug 2012
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What is the value of |x - y|?  [#permalink]

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11 Oct 2017, 08:50
Statement 1 is sufficient for reasons explained above.

Statement 2 is also sufficient because equation can be written as
x(x-1) = xy --> Cross off x on both sides --> x-1=y --> x=y+1

Substitute above in question --> |x - y| = |y + 1 - y|=|1|=1

Intern
Joined: 25 Sep 2017
Posts: 1
Re: What is the value of |x - y|?  [#permalink]

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11 Oct 2017, 12:53
rajudantuluri wrote:
Statement 1 is sufficient for reasons explained above.

Statement 2 is also sufficient because equation can be written as
x(x-1) = xy --> Cross off x on both sides --> x-1=y --> x=y+1

Substitute above in question --> |x - y| = |y + 1 - y|=|1|=1

You can divide by x both sides of the equation if and only if x!=0
We don't know it for sure so we can't divide by x and therefore B is not sufficient and the answer is A
Re: What is the value of |x - y|? &nbs [#permalink] 11 Oct 2017, 12:53
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