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Is m =1? 1)m^3=m 2)m^4=1

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Director
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Is m =1? 1)m^3=m 2)m^4=1 [#permalink] New post 20 Jun 2006, 06:52
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Is m =1?
1)m^3=m
2)m^4=1
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Director
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Re: DS number prop [#permalink] New post 20 Jun 2006, 06:58
Yurik79 wrote:
Is m =1?
1)m^3=m
2)m^4=1


(2) INSUFF because, for e.g. -1^4 = 1^4 =1
(1) m^3 = m*m^2 = m, so again -1 or 1 are probable, INSUFF

combining (1) and (2) m* (m ^3) = 1 => m* (m) = 1, again, -1 or 1 are possible.

(E)
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 [#permalink] New post 20 Jun 2006, 08:58
Is m = 1?
1)m^3=m
if m = 1 => yes,
if m = 13^(1/3) then m^3 = m => no,

=> Not sufficient

2)m^4=1
if m = 1 => yes,
if m = 7 => no, => Not sufficient

(1) & (2):
m^4 = m^3
or m^3(m-1) = 0

or m = 0 or m =1 Still not sufficient.

Answer: E
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 [#permalink] New post 20 Jun 2006, 21:33
Ans is E as m = +/-1 cannot be eliminated even after combining I and II.
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 [#permalink] New post 28 Jun 2006, 15:01
Here's how I solved it:

1: m3 = m
=> m3 - m = 0
=>m(m-1)(m+1)=0

m = 0, 1, -1

So 1 is insufficient.

2: m4=1
=>m = 1, -1

So 2 is sufficient

Combining 1 and 2, m is 1,-1, so still sufficient, therefore E.
  [#permalink] 28 Jun 2006, 15:01
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