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

Question

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

einstein10 · Answer

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

calvinhobbes · Answer

Same logic as the above.

What's the OA?

jusjmkol740 · Answer

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.

einstein10 · Answer

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

jusjmkol740 · Answer

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...

BrushMyQuant · Answer

Bunuel  : Please update OA to A. Thank you

Bunuel · Answer

________________
Done. Thank you.

syahasa2 · Answer

Thought the question was "Is x@y=yx" .
Please correct the typing mistake there.

Nunuboy1994 · Answer

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.

Bunuel · Answer

No. Unless it is explicitly stated otherwise, different variables CAN represent the same number.

KrishnakumarKA1 · Answer

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

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GMAT Data Sufficiency (DS) Questions

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

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