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If a = 222+1 and b = 525+1, how many digits does a·b have?

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If a = 222+1 and b = 525+1, how many digits does a·b have?

by Max@Math Revolution » Thu Jun 18, 2020 11:32 pm

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[GMAT math practice question]

If a = 2^22+1 and b = 5^25+1, how many digits does a·b have?

A. 22
B. 25
C. 27
D. 47
E. 49
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Re: If a = 222+1 and b = 525+1, how many digits does a·b have?

by Max@Math Revolution » Sun Jun 21, 2020 6:20 pm
=>

a·b = (2^22 + 1)(5^25 + 1) = 2^22·5^25 + 5^25 + 2^22 + 1 = 5^3·(2·5)^22 + 5^25 + 2^22 + 1
= 125·10^22 + 5^25 + 2^22 + 1.
Therefore, a·b has 25 digits, as that is the largest exponent.

Therefore, B is the answer.
Answer: B
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