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# If ☉ denotes a mathematical operation, does

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Manager
Joined: 27 Aug 2007
Posts: 210
If ☉ denotes a mathematical operation, does  [#permalink]

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12 Sep 2007, 13:09
If ☉ denotes a mathematical operation, does
x☉y=y☉x for all x and y?

(1) For all x and y, x☉y = 2(x2 + y2).
(2) For all y, 0☉y = 2 y2

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Director
Joined: 03 May 2007
Posts: 668
Schools: University of Chicago, Wharton School

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12 Sep 2007, 13:24
1
Ferihere 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(x2 + y2).
(2) For all y, 0☉y = 2 y2

A.

1: x☉y = 2 (x^2 + y^2)
y☉x = 2 (y^2 + x^2) suff..

2: 0☉y = 2y^2 could also equal to 2(0^2 +y^2), 2(0 +y)^2 or 2(y +0)^2.
so x☉y could equal to 2(x^2+y^2) or 2y^2 or 2(x+y)^2 so insuffffff..
Manager
Joined: 27 Aug 2007
Posts: 210

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12 Sep 2007, 13:35
Fistail wrote:
Ferihere 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(x2 + y2).
(2) For all y, 0☉y = 2 y2

A.

1: x☉y = 2 (x^2 + y^2)
y☉x = 2 (y^2 + x^2) suff..

2: 0☉y = 2y^2 could also equal to 2(0^2 +y^2), 2(0 +y)^2 or 2(y +0)^2.
so x☉y could equal to 2(x^2+y^2) or 2y^2 or 2(x+y)^2 so insuffffff..

answer was not really clear... I still did not get the concept or logic behind...
Director
Joined: 03 May 2007
Posts: 668
Schools: University of Chicago, Wharton School

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12 Sep 2007, 14:11
Ferihere wrote:
Fistail wrote:
Ferihere 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(x2 + y2).
(2) For all y, 0☉y = 2 y2

A.

1: x☉y = 2 (x^2 + y^2)
y☉x = 2 (y^2 + x^2) suff..

2: 0☉y = 2y^2 could also equal to 2(0^2 +y^2), 2(0 +y)^2 or 2(y +0)^2.
so x☉y could equal to 2(x^2+y^2) or 2y^2 or 2(x+y)^2 so insuffffff..

answer was not really clear... I still did not get the concept or logic behind...

1: x☉y = 2 (x^2 + y^2)
y☉x = 2 (y^2 + x^2) suff..

2: 0☉y = 2y^2 = 2(0^2 +y^2) = 2(0 +y)^2 = 2(y +0)^2
if so, x☉y = 2 (x^2+y^2) or 2y^2 or 2(x+y)^2 but they all are not equal.

so x☉y is not equal to y☉x for all x and y. so st 2 is insuff.........

therefore, it is A.
Senior Manager
Joined: 08 Jun 2007
Posts: 477

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12 Sep 2007, 21:13
Fistail wrote:
Ferihere wrote:
Fistail wrote:
[quote="Ferihere"]If ☉ denotes a mathematical operation, does
x☉y=y☉x for all x and y?

(1) For all x and y, x☉y = 2(x2 + y2).
(2) For all y, 0☉y = 2 y2

A.

1: x☉y = 2 (x^2 + y^2)
y☉x = 2 (y^2 + x^2) suff..

2: 0☉y = 2y^2 could also equal to 2(0^2 +y^2), 2(0 +y)^2 or 2(y +0)^2.
so x☉y could equal to 2(x^2+y^2) or 2y^2 or 2(x+y)^2 so insuffffff..

answer was not really clear... I still did not get the concept or logic behind...

1: x☉y = 2 (x^2 + y^2)
y☉x = 2 (y^2 + x^2) suff..

2: 0☉y = 2y^2 = 2(0^2 +y^2) = 2(0 +y)^2 = 2(y +0)^2
if so, x☉y = 2 (x^2+y^2) or 2y^2 or 2(x+y)^2 but they all are not equal.

so x☉y is not equal to y☉x for all x and y. so st 2 is insuff.........

therefore, it is A.[/quote]

I dont think we need to go till that far at all .It seems we are drawing references from stmnt 1 . 0☉y could be anything while representing 0 in that not necessarily just 2(0^2 +y^2)

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Non-Human User
Joined: 09 Sep 2013
Posts: 13318
Re: If ☉ denotes a mathematical operation, does  [#permalink]

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08 Jan 2019, 17:44
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Re: If ☉ denotes a mathematical operation, does   [#permalink] 08 Jan 2019, 17:44
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