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

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If M is a positive integer, then M^3 has how many digits? [#permalink] New post 19 Oct 2007, 04:25
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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
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 [#permalink] New post 19 Oct 2007, 04:28
i am in for B....courtesy: my instincts

So dont ask for detailed solution.............. :-)

OA is E.....any takers???
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 [#permalink] New post 19 Oct 2007, 05:13
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

the answer is (E)

:)
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 [#permalink] New post 19 Oct 2007, 05:21
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

the answer is (E)

:)


You are GOD :-)
  [#permalink] 19 Oct 2007, 05:21
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