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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
Joined: 21 Jan 2007
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Location: New York City
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What is the value of R? 1. R^R = R 2. (1/R)^R = R Can [#permalink]  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
Joined: 03 Sep 2006
Posts: 885
Followers: 6

Kudos [?]: 259 [0], given: 33

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.

What is OA?
Senior Manager
Joined: 01 Sep 2006
Posts: 302
Location: Phoenix, AZ, USA
Followers: 1

Kudos [?]: 15 [0], given: 0

Re: variable base to variable exponent [#permalink]  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
Director
Joined: 03 Sep 2006
Posts: 885
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Kudos [?]: 259 [0], given: 33

Re: variable base to variable exponent [#permalink]  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)?
SVP
Joined: 01 May 2006
Posts: 1805
Followers: 8

Kudos [?]: 99 [0], given: 0

(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.
Director
Joined: 13 Dec 2006
Posts: 521
Location: Indonesia
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Kudos [?]: 105 [0], given: 0

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
SVP
Joined: 01 May 2006
Posts: 1805
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Kudos [?]: 99 [0], given: 0

Re: variable base to variable exponent [#permalink]  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
Joined: 01 Nov 2007
Posts: 69
Followers: 1

Kudos [?]: 3 [0], given: 0

I change my stand to E

thanks Fig
Senior Manager
Joined: 06 Aug 2007
Posts: 370
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Kudos [?]: 23 [0], given: 0

Re: variable base to variable exponent [#permalink]  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
CEO
Joined: 21 Jan 2007
Posts: 2764
Location: New York City
Followers: 9

Kudos [?]: 349 [0], given: 4

Re: variable base to variable exponent [#permalink]  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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