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What is the value of R? 1. R^R = R 2. (1/R)^R = R Can

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CEO
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What is the value of R? 1. R^R = R 2. (1/R)^R = R Can [#permalink] New post 08 Nov 2007, 03:34
What is the value of R?
1. R^R = R
2. (1/R)^R = R

Can someone explain this in detail for me?
Director
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 [#permalink] New post 08 Nov 2007, 04:57
Statement (i) is not sufficient to tell the value of R, which can be 1 or -1. Thus insufficient.

Same in case of statement (ii), R can be 1 and also -1.

Thus answer should be "E".

What is OA?
Senior Manager
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Re: variable base to variable exponent [#permalink] New post 08 Nov 2007, 06:36
bmwhype2 wrote:
What is the value of R?
1. R^R = R
2. (1/R)^R = R

Can someone explain this in detail for me?


Using 1
R^R=R==> R^R-R=0==> R(R^(R-1) -1)=0==>
Either R =0
or R^ (R-1)-1=0==> R^(R-1)=1 i.e. R=1


Using 2

1/R^R=R==> 1=R^(R+1) either R=1 or R=-1

Togather R=1
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Re: variable base to variable exponent [#permalink] New post 08 Nov 2007, 06:44
Damager wrote:
bmwhype2 wrote:
What is the value of R?
1. R^R = R
2. (1/R)^R = R

Can someone explain this in detail for me?


Using 1
R^R=R==> R^R-R=0==> R(R^(R-1) -1)=0==>
Either R =0
or R^ (R-1)-1=0==> R^(R-1)=1 i.e. R=1


Using 2

1/R^R=R==> 1=R^(R+1) either R=1 or R=-1

Togather R=1



Why R=-1 is not possible for the statement (i)?
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 [#permalink] New post 08 Nov 2007, 07:34
(E) for me too :)

R=?

Stat1
We have : R^R = R

o If R=-1, then (-1)^(-1) = -1
o If R=1, then (1)^(1) = 1

INSUFF.

Stat2
(1/R)^R = R

o If R=-1, then (1/(-1))^(-1) = -1
o If R=1, then (1/(1))^(1) = 1

INSUFF.

Both (1) and (2)
We remain with 2 cases : R=1 or R=-1.

INSUFF.
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 [#permalink] New post 08 Nov 2007, 07:38
Answer is E

1. R^R = R is only possible when R is equal to either 1 or -1
2. (1/R)^R = R, here also the equation is true for both 1 an -1

As both are insufficient and together doesn make sense... hence answer is E
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Re: variable base to variable exponent [#permalink] New post 08 Nov 2007, 10:13
sportyrizwan wrote:
Damager wrote:
bmwhype2 wrote:
What is the value of R?
1. R^R = R
2. (1/R)^R = R

Can someone explain this in detail for me?


Using 1
R^R=R==> R^R-R=0==> R(R^(R-1) -1)=0==>
Either R =0
or R^ (R-1)-1=0==> R^(R-1)=1 i.e. R=1


Using 2

1/R^R=R==> 1=R^(R+1) either R=1 or R=-1

Togather R=1



I agree ...C it is


In statment 1, R=-1 works too :)... R^R = (-1)^(-1) = -1 = R....
Manager
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 [#permalink] New post 10 Nov 2007, 11:32
I change my stand to E

thanks Fig
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Re: variable base to variable exponent [#permalink] New post 22 Nov 2007, 18:55
bmwhype2 wrote:
What is the value of R?
1. R^R = R
2. (1/R)^R = R

Can someone explain this in detail for me?


1 . Take R = 0, 1, or -1 all of them will work so not Sufficient.

2. Take R = 1 or -1 it will work so not sufficient..

Together also they dont give you one solution.

So E
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Re: variable base to variable exponent [#permalink] New post 22 Nov 2007, 18:56
spider wrote:
bmwhype2 wrote:
What is the value of R?
1. R^R = R
2. (1/R)^R = R

Can someone explain this in detail for me?


1 . Take R = 0, 1, or -1 all of them will work so not Sufficient.

2. Take R = 1 or -1 it will work so not sufficient..

Together also they dont give you one solution.

So E


0^0 is not valid in gmatland
Re: variable base to variable exponent   [#permalink] 22 Nov 2007, 18:56
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