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

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Director
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If M is a positive integer, then M^3 has how many digits? [#permalink]  04 Jul 2009, 21:45
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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
Manager
Joined: 28 Jan 2004
Posts: 210
Location: India
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Kudos [?]: 9 [0], given: 4

Re: Digits [#permalink]  05 Jul 2009, 00:01
I think E

Stmt 1 -
M can be 100 or 999. In these 2 case the number of digits will be different. Insuff.

Stmt 2 -
M^2 has 5 digits.
This is only possible if M >= 100 and <= 316.
However
If M = 100 the M^3 has 1000000 = 7 digits
If M = 316 then M^3 has 31554496 = 8 digits
Insuff.
Director
Joined: 04 Jan 2008
Posts: 925
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Kudos [?]: 91 [0], given: 14

Re: Digits [#permalink]  05 Jul 2009, 00:02
Is it
[Reveal] Spoiler:
E?

(1) saying M could be
100 or 999

hence M^3 will have 6 and 9 digits resp

(2) saying M^2 could be 10,000 or 99,999

=>M could be 100 or say 3XX

Economist wrote:
If M is a positive integer, then M^3 has how many digits?
(1) M has 3 digits.
(2) M^2 has 5 digits

_________________
Re: Digits   [#permalink] 05 Jul 2009, 00:02
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