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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: 46284
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
00:00

Difficulty:

55% (hard)

Question Stats:

59% (01:10) correct 41% (01:35) wrong based on 62 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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Joined: 18 Aug 2016
Posts: 634
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
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
2
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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If ⊙ denotes a mathematical operation, does x⊙y = y⊙x for all x and y?   [#permalink] 10 Aug 2017, 01:58
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