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M05#26

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M05#26 [#permalink] New post 23 Mar 2010, 19:14
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.
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Re: M05#26 [#permalink] New post 25 Mar 2010, 17:50
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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Re: M05#26 [#permalink] New post 25 Mar 2010, 20:50
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, 20:50
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