If m is a positive integer

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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.

What is the best way to determine if the statements are sufficient?

OA E

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Hi lheiannie07,

We're told that M is a positive integer. We're asked for the number of digits that M^3 has. This question can be solved by TESTing VALUES.

1) M has 3 digits.

IF....
M=100, then M^3 = 1,000,000 and the answer to the question is 7
M=300, then M^3 = 27,000,000 and the answer to the question is 8
Fact 1 is INSUFFICIENT

2) M^2 has 5 digits

The same values that we used in Fact 1 also 'fit' Fact 2:
M=100, M^2=10,000 and M^3 = 1,000,000 and the answer to the question is 7
M=300, M^2=90,000 and M^3 = 27,000,000 and the answer to the question is 8
Fact 2 is INSUFFICIENT

Combined, there's no more work needed. We already have two values that 'fit' both Facts and produce two different answers.
Combined, INSUFFICIENT

Final Answer: E

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