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If ☉ denotes a mathematical operation, does

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Senior Manager
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If ☉ denotes a mathematical operation, does  [#permalink]

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New post 12 Sep 2007, 12:09
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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Re: Confusing question...  [#permalink]

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New post 12 Sep 2007, 12:24
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..
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Re: Confusing question...  [#permalink]

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New post 12 Sep 2007, 12:35
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
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Re: Confusing question...  [#permalink]

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New post 12 Sep 2007, 13:11
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.
Director
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Re: Confusing question...  [#permalink]

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New post 12 Sep 2007, 20:13
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.
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Re: If ☉ denotes a mathematical operation, does  [#permalink]

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New post 08 Jan 2019, 16:44
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Re: If ☉ denotes a mathematical operation, does &nbs [#permalink] 08 Jan 2019, 16:44
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