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Is x y = y x, for all real values of x and y?

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jusjmkol740
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Is x y = y x, for all real values of x and y? [#permalink] New post   Updated on: 07 Oct 2016, 07:35
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Is x @ y = y @ x , for all real values of x and y?

(1) x @ y = 1/x + 1/y
(2) x @ y = x - y
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A

Originally posted by jusjmkol740 on 19 Apr 2010, 01:52.
Last edited by Bunuel on 07 Oct 2016, 07:35, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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einstein10
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Re: Is x y = y x, for all real values of x and y? [#permalink] New post   19 Apr 2010, 02:01
jusjmkol740 wrote:
Is x @ y = y @ x, for all real values of x and y?

Stmt 1: x @ y = 1/x + 1/y
Stmt 2: x @ y = x - y


stmt1: x@y = 1/x+1/y ------->( 1)
also, y@x= 1/y+1/x ------(2)
from (1) and (2) x@y = y@x ==>suff

stmt2 clearly x@y is not equal to y@x except when x=y=0 in that case
x@y= y@x => insuff.

IMO A
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Re: Is x y = y x, for all real values of x and y? [#permalink] New post   19 Apr 2010, 02:53
Same logic as the above.

What's the OA?
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Re: Is x y = y x, for all real values of x and y? [#permalink] New post   20 Apr 2010, 05:50
I really don't have the OA. Apologies for that.

Actually I also came up with the same answer i.e. A.

But 2 things bothering me:
1) the question asks about "all real values of x and y".... when x = y = 0, is the 1st stmt valid?
2) the question is a "yes/ no" type. in that case can't we say that the answer to the question is "NO" as per stmt 2. thus, can't we say that stmt 2 is also sufficient to answer the question?

Let me know. Thanks.
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Re: Is x y = y x, for all real values of x and y? [#permalink] New post   20 Apr 2010, 10:12
jusjmkol740 wrote:
I really don't have the OA. Apologies for that.

Actually I also came up with the same answer i.e. A.

But 2 things bothering me:
1) the question asks about "all real values of x and y".... when x = y = 0, is the 1st stmt valid?
2) the question is a "yes/ no" type. in that case can't we say that the answer to the question is "NO" as per stmt 2. thus, can't we say that stmt 2 is also sufficient to answer the question?

Let me know. Thanks.

you nicely pointed out. what is the source of this problem? before posting i gave thought about x=y=0 for first stmt but since generally as a rule when ever variable is in denominator, it should be mentioned that it is not equals to zero.
since it is not mentioned we can assume it is not equal to zero but again if we assume x=y !=0 then stmt will also confirm and then the answer will be D. so i think answer more towards D instead A :)
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jusjmkol740
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Re: Is x y = y x, for all real values of x and y? [#permalink] New post   20 Apr 2010, 14:28
A friend of mine faced this question in one of the GMAT tutorials.

However, since it is not mentioned that x and y =! 0, i don't think it is safe to assume that in a DS question.

The question is also a bit confusing as it asks whether the condition is true for all values of x and y. St 1 gives us "yes" when x and y are not equal to 0; while St 2 gives us "yes" only when x and y are equal to 0.

I'm still looking for the "right answer". Any help is most welcome...
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Re: Is x y = y x, for all real values of x and y? [#permalink] New post   14 Sep 2016, 08:50
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Bunuel : Please update OA to A. Thank you
jusjmkol740 wrote:
Is x @ y = y x, for all real values of x and y?

Stmt 1: x @ y = 1/x + 1/y
Stmt 2: x @ y = x - y
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Re: Is x y = y x, for all real values of x and y? [#permalink] New post   14 Sep 2016, 09:10
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BrushMyQuant wrote:
Bunuel : Please update OA to A. Thank you
jusjmkol740 wrote:
Is x @ y = y x, for all real values of x and y?

Stmt 1: x @ y = 1/x + 1/y
Stmt 2: x @ y = x - y

________________
Done. Thank you.
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Re: Is x y = y x, for all real values of x and y? [#permalink] New post   07 Oct 2016, 07:32
jusjmkol740 wrote:
Is x @ y = y x, for all real values of x and y?

(1) x @ y = 1/x + 1/y
(2) x @ y = x - y



Thought the question was "Is x@y=yx" .
Please correct the typing mistake there.
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Re: Is x y = y x, for all real values of x and y? [#permalink] New post   22 Feb 2017, 15:12
Does x @ y imply that x and y cannot be the same integer? As in you cannot have 1 1 for x and y? In that case A makes sense.
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Re: Is x y = y x, for all real values of x and y? [#permalink] New post   23 Feb 2017, 00:38
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Nunuboy1994 wrote:
Does x @ y imply that x and y cannot be the same integer? As in you cannot have 1 1 for x and y? In that case A makes sense.


No. Unless it is explicitly stated otherwise, different variables CAN represent the same number.
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Re: Is x y = y x, for all real values of x and y? [#permalink] New post   23 Feb 2017, 03:47
Prompt analysis
@ is an variable operator between x and y

Superset
The answer will be either yes or no

Translation
In order to find the answer, we need:
1# the exact operator represented by @
2# any other condition with this operator

Statement analysis

St 1: x @ y = 1/x + 1/y. therefore y @ x= 1/y + 1/x = x @ y.YES. Answer
St 2: x @ y = x - y. Therefore y @ x = y - x = - x @ y.NO. but it will be valid if x = y. INSUFFICIENT

Option A
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Re: Is x y = y x, for all real values of x and y? [#permalink] New post   31 Dec 2021, 11:02
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Re: Is x y = y x, for all real values of x and y? [#permalink]
31 Dec 2021, 11:02
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