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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: 56306
If ⊙ denotes a mathematical operation, does x⊙y = y⊙x for all x and y?  [#permalink]

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10 Aug 2017, 01:41
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45% (medium)

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63% (01:27) correct 37% (01:50) wrong based on 170 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, 01:58
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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: 12 Mar 2019
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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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04 Jul 2019, 06:00
Can someone provide a better explanation of this? Bunuel ?
Re: If ⊙ denotes a mathematical operation, does x⊙y = y⊙x for all x and y?   [#permalink] 04 Jul 2019, 06:00
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