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# If (x − y)^2 = x^2 + y^2 , then which one of the following statements

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Math Expert
Joined: 02 Sep 2009
Posts: 61192
If (x − y)^2 = x^2 + y^2 , then which one of the following statements  [#permalink]

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Updated on: 08 Jul 2019, 00:24
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Difficulty:

5% (low)

Question Stats:

78% (00:58) correct 22% (01:27) wrong based on 89 sessions

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If $$(x − y)^2 = x^2 + y^2$$, then which one of the following statements must also be true?

I. x = 0
II. y = 0
III. xy = 0

(A) None
(B) I only
(C) II only
(D) III only
(E) II and III only

Source: Nova GMAT
Difficulty Level: 500

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Originally posted by Bunuel on 01 Jun 2017, 11:08.
Last edited by SajjadAhmad on 08 Jul 2019, 00:24, edited 1 time in total.
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4318
Re: If (x − y)^2 = x^2 + y^2 , then which one of the following statements  [#permalink]

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01 Jun 2017, 11:57
Top Contributor
Bunuel wrote:
If $$(x − y)^2 = x^2 + y^2$$, then which one of the following statements must also be true?

I. x = 0
II. y = 0
III. xy = 0

(A) None
(B) I only
(C) II only
(D) III only
(E) II and III only

Given: (x − y)² = x² + y²
Expand the left side to get: x² - xy - xy + y² = x² + y²
Simplify the left side to get: x² - 2xy + y² = x² + y²
Subtract x² from both sides: -2xy + y² = y²
Subtract y² from both sides: -2xy = 0
Divide both sides by -2 to get: xy = 0

So, III is true.
However, just because xy = 0, we can't say for sure whether x = 0 or y = 0.
All we know is that at least one of those variables equals 0.

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Re: If (x − y)^2 = x^2 + y^2 , then which one of the following statements   [#permalink] 01 Jun 2017, 11:57
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