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# If ⊙ denotes a mathematical operation, does x⊙y = y⊙x for all x and y?

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Math Expert
Joined: 02 Sep 2009
Posts: 52386
If ⊙ denotes a mathematical operation, does x⊙y = y⊙x for all x and y?  [#permalink]

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10 Aug 2017, 00:41
00:00

Difficulty:

45% (medium)

Question Stats:

63% (01:10) correct 37% (01:27) wrong based on 111 sessions

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If ⊙ denotes a mathematical operation, does $$x⊙y = y⊙x$$ for all x and y?

(1) For all x and y, $$x ⊙ y = 2(x^2 + y^2)$$

(2) For all y, $$0 ⊙ y = 2y^2$$

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If ⊙ denotes a mathematical operation, does x⊙y = y⊙x for all x and y?  [#permalink]

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10 Aug 2017, 00:58
2
1
Bunuel wrote:
If ⊙ denotes a mathematical operation, does $$x⊙y = y⊙x$$ for all x and y?

(1) For all x and y, $$x ⊙ y = 2(x^2 + y^2)$$

(2) For all y, $$0 ⊙ y = 2y^2$$

(1) since x and y can be interchanged
Sufficient

(2) if ⊙ denotes +
then
0 ⊙ y = 0 + 2y^2
x ⊙ y = x + 2y^2
Here x and y cannot be interchanged
but if
0 ⊙ y = 2*0^2 + 2y^2
x ⊙ y = 2*x^2 + 2y^2
Here x and y can be interchanged
Not Sufficient

A
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Luckisnoexcuse

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Joined: 09 Sep 2013
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Re: If ⊙ denotes a mathematical operation, does x⊙y = y⊙x for all x and y?  [#permalink]

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08 Jan 2019, 16:40
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If ⊙ denotes a mathematical operation, does x⊙y = y⊙x for all x and y? &nbs [#permalink] 08 Jan 2019, 16:40
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