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# M05#26

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Manager
Joined: 05 Dec 2009
Posts: 127
Followers: 2

Kudos [?]: 86 [0], given: 0

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23 Mar 2010, 20:14
What is the value of $$R$$ ?

1. $$R^R = R$$
2. $$(\frac{1}{R})^R = R$$

As per GMAT club explanation, as per both stmt1 and stmt2 R = 1 or -1...but as per my calc, stmt1: R should be 0 or 1.
and as per S2 R should be 1 or -1
So by combining 2 stmt, R = 1. So C should be the ans.

Can someone pls help me to understand.
Manager
Joined: 20 Mar 2010
Posts: 84
Followers: 2

Kudos [?]: 83 [0], given: 1

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25 Mar 2010, 18:50
xyztroy wrote:
What is the value of $$R$$ ?

1. $$R^R = R$$
2. $$(\frac{1}{R})^R = R$$

As per GMAT club explanation, as per both stmt1 and stmt2 R = 1 or -1...but as per my calc, stmt1: R should be 0 or 1.
and as per S2 R should be 1 or -1
So by combining 2 stmt, R = 1. So C should be the ans.

Can someone pls help me to understand.

0^0 is undefined. Also (-1) ^ -1 = (1/(-1)^1) = -1. So R can be -1 or 1 as per stmt1

Thanks
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Manager
Joined: 05 Dec 2009
Posts: 127
Followers: 2

Kudos [?]: 86 [0], given: 0

### Show Tags

25 Mar 2010, 21:50
crack700 wrote:
xyztroy wrote:
What is the value of $$R$$ ?

1. $$R^R = R$$
2. $$(\frac{1}{R})^R = R$$

As per GMAT club explanation, as per both stmt1 and stmt2 R = 1 or -1...but as per my calc, stmt1: R should be 0 or 1.
and as per S2 R should be 1 or -1
So by combining 2 stmt, R = 1. So C should be the ans.

Can someone pls help me to understand.

0^0 is undefined. Also (-1) ^ -1 = (1/(-1)^1) = -1. So R can be -1 or 1 as per stmt1

Thanks

$$R^R = R$$
$$R^R - R = 0$$
$$R[R^(R-1) - 1] = 0$$

so R = 0 or $$[R^(R-1) = 1]$$ which is possible only if R =1 or R-1 = 0.
Re: M05#26   [#permalink] 25 Mar 2010, 21:50
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# M05#26

Moderator: Bunuel

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