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What is the sum of the digits of the number (2^{2018})(5^{20

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What is the sum of the digits of the number (2^{2018})(5^{20

by Max@Math Revolution » Thu Feb 07, 2019 12:42 am

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[GMAT math practice question]

What is the sum of the digits of the number (2^{2018})(5^{2019})(3^2)?

A. 4
B. 5
C. 6
D. 7
E. 9
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by Brent@GMATPrepNow » Thu Feb 07, 2019 11:49 am
Max@Math Revolution wrote:[GMAT math practice question]

What is the sum of the digits of the number (2^{2018})(5^{2019})(3^2)?

A. 4
B. 5
C. 6
D. 7
E. 9
Useful rule: (x^k)(y^k) = (xy)^k
Example: (3^4)(7^4) = 21^4

(2^2018)(5^2019)(3^2) = (2^2018)((5^2018)(5^1))(3^2)
= (2^2018)(5^2018)(5^1))(3^2)
= (10^2018)(5^1))(3^2)
= (10^2018)(5)(9)
= (10^2018)(45)


We know that (10^2018) = 1 followed by 2018 zeros
So, (10^2018)(45) = 45 followed by 2018 zeros

In other words, (10^2018)(45) = 450000000000000000000000000000000000000000......

Sum of digits = 4 + 5 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + ........
= 9

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Sun Feb 10, 2019 4:54 pm
=>

(2^{2018})(5^{2019})(3^2)
= (2^{2018})(5^{2019})(5^1)(3^2)
= (10^{2018})(5)(9)
= (45)(10^{2018})
= 450000...0

The sum of the digits is
4 + 5 + 0 + 0 + 0 + ... + 0 = 9

Therefore, the answer is E.
Answer: E
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