[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
What is the sum of the digits of the number (2^{2018})(5^{20
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- Max@Math Revolution
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Useful rule: (x^k)(y^k) = (xy)^kMax@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
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
- Max@Math Revolution
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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})
= 450000...0
The sum of the digits is
4 + 5 + 0 + 0 + 0 + ... + 0 = 9
Therefore, the answer is E.
Answer: E
(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
Math Revolution
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Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
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