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1) M has 3 digits --> M e (100,999) --> M^3 has from 6 to 8 digits. insufficient. 2) M^2 has 5 digits --> M e (~330,999) --> consider two integers: 400 and 900 ---> M^3 is 64*1000000 and 729*1000000. insufficient.

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

1) M has 3 digits 2) M^2 has 5 digits

1: take minimum and max. value for 3 digit integers min value if m = 100, M^3 = 1,000,000, which has 7 digits. min value if m = 999, M^3 = do not know exactly but should have 9 digits (since 1000^3 has 10 digits, 999 is slight lower than 1000. so 999^3 should have 9 digits). not suff...

2: again min and max. values for m^2 that has 5 digits. min value of m^2 = 10,000.00, m = 100 and m^3 = 1,000,000, which is the same as above in 1. min value if m^2 = 99,999, m = 316 approx. again do not know exactly the value of m^3 but it should have either 9 or 8 digits. again not suff.