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M9 #21

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Director
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Joined: 11 Jun 2007
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M9 #21 [#permalink] New post 20 Sep 2009, 23:51
If the operation # satisfies X#Y = \frac{1}{X#Y} for any non-zero number X and Y , which of the following can be # ?

1. X#Y = \frac{1}{XY}
2. X#Y = \frac{X}{Y}
3. X#Y = XY

I understood the answer how X#Y can only be 1 or -1 but can someone explain why 1, 2, or 3 could not equal 1 or -1. Thanks.
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Re: M9 #21 [#permalink] New post 28 Sep 2009, 11:15
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Can you post the entire question.

1. 1/XY=XY
2. X/Y = Y/X
3. XY = 1/XY (same as No. 1)

These are the 3 condition. Now for condition 2. X & Y does not have to be just 1 or -1 it can be any integer as long as X=Y
for example X=2 Y=2 -> X/Y is Y/X

but for 1 & 3 X & Y can be only 1 or -1.
you should also take fraction since it does not say integer.

What are the answer choices?
Re: M9 #21   [#permalink] 28 Sep 2009, 11:15
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M9 #21

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