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Find a nonzero integer R. (1) R^3=R^R (2) |R^R|=1

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SVP
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Joined: 03 Feb 2003
Posts: 1603

Kudos [?]: 303 [0], given: 0

Find a nonzero integer R. (1) R^3=R^R (2) |R^R|=1 [#permalink]

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New post 13 Jul 2003, 07:59
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A
B
C
D
E

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(N/A)

Question Stats:

50% (00:53) correct 50% (01:09) wrong based on 4 sessions

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Find a nonzero integer R.

(1) R^3=R^R
(2) |R^R|=1

Kudos [?]: 303 [0], given: 0

Director
Director
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Joined: 03 Jul 2003
Posts: 651

Kudos [?]: 104 [0], given: 0

 [#permalink]

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New post 13 Jul 2003, 17:21
Your questions are too good! Keep it rolling !!

My Ans:
From 1: R = 3, 1, and тАУ1
From 2: R = 1, and тАУ1
From Both: R = 1 and тАУ1

Thus Ans: E

Kudos [?]: 104 [0], given: 0

SVP
SVP
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Joined: 16 Nov 2010
Posts: 1597

Kudos [?]: 592 [0], given: 36

Location: United States (IN)
Concentration: Strategy, Technology
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Re: DS: OLD [#permalink]

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New post 20 Mar 2011, 03:38
From (1), the answer can be 3, 1 and -1

From (2), the answer can be -1 and 1

From (1) and (2), the answer can be -1 or 1, so the answer is E.
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Kudos [?]: 592 [0], given: 36

Manager
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Joined: 05 Jan 2011
Posts: 171

Kudos [?]: 188 [0], given: 8

Re: DS: OLD [#permalink]

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New post 20 Mar 2011, 07:38
subhashghosh wrote:
From (1), the answer can be 3, 1 and -1

From (2), the answer can be -1 and 1

From (1) and (2), the answer can be -1 or 1, so the answer is E.


is there Any algebraic approach to solve R^3=R^R to get 3, 1, -1?
R^3=R^R
Equating powers R=3
How to get 1 ,-1?

Kudos [?]: 188 [0], given: 8

SVP
SVP
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Joined: 16 Nov 2010
Posts: 1597

Kudos [?]: 592 [0], given: 36

Location: United States (IN)
Concentration: Strategy, Technology
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Re: DS: OLD [#permalink]

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New post 20 Mar 2011, 07:47
You don't need algebra, it's obvious that for R^3=R^R:

3^3 = 3^3 (R = 3)

1^3 = 1^3

(-1)^3 = (-1) ^(-1) = 1/(-1) = -1
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Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

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Kudos [?]: 592 [0], given: 36

Re: DS: OLD   [#permalink] 20 Mar 2011, 07:47
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Find a nonzero integer R. (1) R^3=R^R (2) |R^R|=1

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