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

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

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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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New post 10 Aug 2017, 00:58
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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

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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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New post 04 Jan 2020, 22:02
(1) For all x and y, x⊙y=2(x2+y2)

Here X and Y are interchangeable and gives the same value. Hence sufficient.

(2) For all y, 0⊙y=2y2

here y⊙0=0 , the values are not equal if y has values other than 0. Hence insufficient.
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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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New post 14 Jan 2020, 23:38
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, \(0 ⊙ y = 2y^2\)


DS17602.01


Bunuel can u explain this qsn ,sply 2nd stmnt?
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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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New post 26 Jan 2020, 20:13
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vanam52923 wrote:
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, \(0 ⊙ y = 2y^2\)


DS17602.01


Bunuel can u explain this qsn ,sply 2nd stmnt?

Can any one explain this question?
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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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New post 13 Mar 2020, 04:26
vanam52923 wrote:
vanam52923 wrote:
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, \(0 ⊙ y = 2y^2\)


DS17602.01


Bunuel can u explain this qsn ,sply 2nd stmnt?

Can any one explain this question?


VeritasKarishma Bunuel Can you please explain the solution for this question? Thanks!
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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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New post 24 Apr 2020, 10:25
Could we replace "operation" by "function" here ? I cannot understand what's going on.

I understand that if we have x o y = 2(x^2+y^2) we can change the order and come up with x o y = y o x. But which of "+", "-", "/" and "*" could work with "all x and all y". I cannot understand why we use an equal sign.
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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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New post 06 Jun 2020, 21:14
For st 2, we can see that 0 to any nonzero power = 0 and thus 0•2y^2=2y^2
Thus when we replace 0 with x, then x can technically take any power.

However, when x takes any power, then sometimes it CANNOT be interchanged with y eg. 2(X^3+y^2)≠2(y^3+x^2) for say y=2 and x=3 [ie. 2(27+4)≠2(8+9)]

But sometimes it CAN be interchanged with y^2, ie. When x has the power 2. Not Sufficient

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

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New post 18 Jun 2020, 08:34
OFFICIAL EXPLANATION

1) For all x and y, \(x⊙y = 2(x^2 + y^2)\) is equal to \(y⊙x = 2(y^2 + x^2)\); SUFFICIENT.

2) If \(x⊙y = 2(x^2+y^2)\) for all x and y, then \( 0⊙y = 2y^2\) for all y and x⊙y = y⊙x for all x and y. However, if \(x⊙ y = 2(x^3 + y^2)\) for all x and y, then \(0⊙y = 2y^2\) for all y, but\( 1⊙2 = 2(1^3) + 2(2^2) = 10\) and \(2⊙1
= 2(2^3) + 2(1^2) = 18; \)NOT sufficient.

The correct answer is A;
statement 1 alone is sufficient.
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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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New post 24 Jun 2020, 13:19
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, \(0 ⊙ y = 2y^2\)


DS17602.01

anyone got a PROPER. COMPREHENSIBLE. CLEAR solution for this. none of the posts in the thread deliver
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If ⊙ denotes a mathematical operation, does x⊙y = y⊙x for all x and y?  [#permalink]

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New post 08 Jul 2020, 23:56
chetan2u VeritasKarishma GMATBusters

For statement 2, isn't this logic sufficient that the expression only holds true when one of the variables (be it x or y) is 0 whereas the questions asks if it is true for all values of x and y ?

On a related note, is the expression in statement 2 even interchangeable ? I mean the expression hold strictly when x is 0 and y is a variable. Since one of the values is fixed, doesn't that mean that the expression can't be interchanged (i.e x for y and y for as can be done in Statement 1).

Will appreciate some comments to improve my logic here.
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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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New post 13 Jul 2020, 08:26
altairahmad wrote:
chetan2u VeritasKarishma GMATBusters

For statement 2, isn't this logic sufficient that the expression only holds true when one of the variables (be it x or y) is 0 whereas the questions asks if it is true for all values of x and y ?

On a related note, is the expression in statement 2 even interchangeable ? I mean the expression hold strictly when x is 0 and y is a variable. Since one of the values is fixed, doesn't that mean that the expression can't be interchanged (i.e x for y and y for as can be done in Statement 1).

Will appreciate some comments to improve my logic here.


(2) For all y,
0⊙y=2y^2

The user defined operator could stand for anything. It is possible that

x⊙y = 2y^2 + x (not symmetrical)
Then 0⊙y = 2y^2

It is also possible that x⊙y = 2y^2 + 2x^2 (symmetrical)
Then also 0⊙y = 2y^2

In one case, x⊙y=y⊙x, in one it is not. Hence not sufficient.
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Re: If ⊙ denotes a mathematical operation, does x⊙y = y⊙x for all x and y?   [#permalink] 13 Jul 2020, 08:26

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

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