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# If M is a positive integer, then M^3 has how many digits?

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Senior Manager
Joined: 11 Sep 2005
Posts: 329
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If M is a positive integer, then M^3 has how many digits? [#permalink]  19 Oct 2007, 03:25
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If M is a positive integer, then M^3 has how many digits?

(1) M has 3 digits.
(2) M^2 has 5 digits
Senior Manager
Joined: 11 Sep 2005
Posts: 329
Followers: 1

Kudos [?]: 42 [0], given: 0

i am in for B....courtesy: my instincts

So dont ask for detailed solution..............

OA is E.....any takers???
VP
Joined: 08 Jun 2005
Posts: 1147
Followers: 6

Kudos [?]: 128 [0], given: 0

statement 1

M can be 111 or 999 so:

100*100*100 = 10*10*10*10*10*10 = 10^6 --> six digits number

1000*1000*1000 = 10*10*10*10*10*10*10*10*10 = 10^9 ---> eight digits number

insufficient

statement 1

10000 or 99999

10,000 = 100*100

100,000 = sqrt(100,000)*sqrt(100,000)

so either 100^3 or sqrt(100,000)^3

insufficient

Senior Manager
Joined: 11 Sep 2005
Posts: 329
Followers: 1

Kudos [?]: 42 [0], given: 0

KillerSquirrel wrote:
statement 1

M can be 111 or 999 so:

100*100*100 = 10*10*10*10*10*10 = 10^6 --> six digits number

1000*1000*1000 = 10*10*10*10*10*10*10*10*10 = 10^9 ---> eight digits number

insufficient

statement 1

10000 or 99999

10,000 = 100*100

100,000 = sqrt(100,000)*sqrt(100,000)

so either 100^3 or sqrt(100,000)^3

insufficient

You are GOD
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