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# M9 #21

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Director
Joined: 11 Jun 2007
Posts: 920
Followers: 1

Kudos [?]: 206 [0], given: 0

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21 Sep 2009, 00:51
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.
Manager
Joined: 08 Nov 2005
Posts: 181
Followers: 2

Kudos [?]: 21 [1] , given: 10

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28 Sep 2009, 12:15
1
KUDOS
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.

Manager
Joined: 23 Jan 2013
Posts: 172
Concentration: Technology, Other
Schools: Haas
GMAT Date: 01-14-2015
WE: Information Technology (Computer Software)
Followers: 3

Kudos [?]: 48 [0], given: 41

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01 Jun 2014, 05:24
If the operation # satisfies X # Y = 1/(X # Y) for any non-zero number X and Y, which of the following can be #?

1. X # Y = 1/XY
2. X # Y = X/Y
3. X # Y = XY

None
1 only
2 only
1 and 2 only
1 and 3 only

I still cannot figure this question out , can anyone help me out here ?
Math Expert
Joined: 02 Sep 2009
Posts: 38921
Followers: 7744

Kudos [?]: 106368 [0], given: 11622

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01 Jun 2014, 05:37
shelrod007 wrote:
If the operation # satisfies X # Y = 1/(X # Y) for any non-zero number X and Y, which of the following can be #?

1. X # Y = 1/XY
2. X # Y = X/Y
3. X # Y = XY

None
1 only
2 only
1 and 2 only
1 and 3 only

I still cannot figure this question out , can anyone help me out here ?

This question was removed from data base. So, don't worry about it.
_________________
Re: M9 #21   [#permalink] 01 Jun 2014, 05:37
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# M9 #21

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