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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## What is the sum of the digits of the number (2^{2018})(5^{20 tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## What is the sum of the digits of the number (2^{2018})(5^{20 ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [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 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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### GMAT/MBA Expert

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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

Cheers,
Brent

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=>

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

The sum of the digits is
4 + 5 + 0 + 0 + 0 + â€¦ + 0 = 9

_________________

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