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# Define x?y to be |x - y| for all real numbers x and y. Which of the fo

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Math Expert
Joined: 02 Sep 2009
Posts: 60460
Define x?y to be |x - y| for all real numbers x and y. Which of the fo  [#permalink]

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19 Mar 2019, 02:07
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Difficulty:

75% (hard)

Question Stats:

38% (01:32) correct 62% (01:43) wrong based on 60 sessions

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Define x?y to be |x - y| for all real numbers x and y. Which of the following statements is not true?

(A) x?y = y?x for all x and y

(B) 2(x?y) = (2x)?(2y) for all x and y

(C) x?0 = x for all x

(D) x?x = 0 for all x

(E) x?y > 0 if $$x \neq y$$

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Joined: 18 Aug 2017
Posts: 5691
Location: India
Concentration: Sustainability, Marketing
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WE: Marketing (Energy and Utilities)
Re: Define x?y to be |x - y| for all real numbers x and y. Which of the fo  [#permalink]

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19 Mar 2019, 06:06
Bunuel wrote:
Define x?y to be |x - y| for all real numbers x and y. Which of the following statements is not true?

(A) x?y = y?x for all x and y

(B) 2(x?y) = (2x)?(2y) for all x and y

(C) x?0 = x for all x

(D) x?x = 0 for all x

(E) x?y > 0 if $$x \neq y$$

for x?0 = x for all x
0>x
not sufficient
IMO C
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Joined: 27 May 2012
Posts: 944
Re: Define x?y to be |x - y| for all real numbers x and y. Which of the fo  [#permalink]

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19 Mar 2019, 11:56
Bunuel wrote:
Define x?y to be |x - y| for all real numbers x and y. Which of the following statements is not true?

(A) x?y = y?x for all x and y

(B) 2(x?y) = (2x)?(2y) for all x and y

(C) x?0 = x for all x

(D) x?x = 0 for all x

(E) x?y > 0 if $$x \neq y$$

Yes if X = -2 then x?y
|-2-0|=2 which is $$\neq$$ -2
Hence C is not true .
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- Stne
Re: Define x?y to be |x - y| for all real numbers x and y. Which of the fo   [#permalink] 19 Mar 2019, 11:56
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