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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Define x?y to be |x - y| for all real numbers x and y. Which of the fo

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Math Expert V
Joined: 02 Sep 2009
Posts: 59561
Define x?y to be |x - y| for all real numbers x and y. Which of the fo  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 37% (01:36) correct 63% (01:42) wrong based on 56 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 $$x \neq y$$
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5428
Location: India
Concentration: Sustainability, Marketing
GPA: 4
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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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
Director  V
Joined: 27 May 2012
Posts: 945
Re: Define x?y to be |x - y| for all real numbers x and y. Which of the fo  [#permalink]

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