Symbols-problem question

[anand108]

Let # denote a mathematical operation. Is it true that x#y = y#x for all x and y?

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

My answer:
(1) YES, because commutative property of addition: (1/x)+(1/y) = (1/y)+(1/x)
(2) NO, because x-y not equal to y-x. But what if we take the number 0; then x-y=y-x (0-0=0-0). So (2) is not sufficient and answer could be A

The book (NOVA's GMAT Prep Course) says that the answer is D.

Can anyone please help?

[\'manpreet singh]

Hi Anand,

Statement 1:
Your reasoning is correct, as statement one is sufficient due to commutative property of addition.

Statement 2 can be analysed putting value X=5,Y=3
X-Y=2
Y-X=-2

So here x#y not = y#x for all X and Y.
Hence it answers the question( Is it true that x#y = y#x for all x and y?)Answer is No.
Remember this is Yes-No question of data sufficiency.You only need to definitively answers yes or no without doubt.


So answer is D(both statements are sufficient alone)

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Manpreet

[anand108]

Right. So my question is: what if x=y=0? Then the (2)becomes inconsistent, doesn't it?

[jcnasia]

Right. So my question is: what if x=y=0? Then the (2)becomes inconsistent, doesn't it?

The question that is asked is: Is it true that x#y = y#x for all x and y?
If x#y=x-y, then does x#y = y#x for all x and y?

manpreet singh is correct...we can answer definitively that it is not true for all x and y. It doesn't matter whether it's true for x=y=0. We want to know whether it is true for all x and y, and it is not.

I came back and edited this answer after I saw how it was written.
The red text above is written ambiguously. The opposite of 'x#y = y#x is true for all x and y' is 'there exists x and y that x#y = y#x is false'.

[Anurag@Gurome]

Let # denote a mathematical operation. Is it true that x#y = y#x for all x and y?

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

Statement 1: x#y = (1/x) + (1/y) = (1/y) + (1/x) = y#x
Hence, it is true that for all x and y, x#y = y#x.
Hence, answer to the question is YES.

Sufficient

Statement 2: x#y = (x - y) and y#x = (y - x)
If x = y = 0, then x#y = y#x
Otherwise, x#y ≠ y#x
Hence, it is not true that for all x and y, x#y = y#x.
Hence, answer to the question is NO.

Sufficient

The correct answer is D.

Note : This is not a proper GMAT DS question. In GMAT you will never find a DS question in whih two statements leads to different answers to the original question.