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

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Math Expert
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What is the value of |x - y|? [#permalink]

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09 Oct 2017, 23:55
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Question Stats:

60% (01:00) correct 40% (00:49) wrong based on 38 sessions

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What is the value of |x - y|?

(1) $$–2xy – y^2 = x^2 – 4xy – 1$$

(2) $$x^2 – x = xy$$
[Reveal] Spoiler: OA

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Re: What is the value of |x - y|? [#permalink]

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10 Oct 2017, 00:55
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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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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

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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

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Re: What is the value of |x - y|?   [#permalink] 11 Oct 2017, 12:53
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