Difference between revisions of "2023 AMC 12A Problems/Problem 4"

(Video Solution)
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~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)
 
~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)
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==Video Solution (Quick and Easy!)==
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https://youtu.be/Xy8vyymlPBg
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~Education, the Study of Everything
  
 
==See Also==
 
==See Also==

Revision as of 14:41, 11 November 2023

The following problem is from both the 2023 AMC 10A #5 and 2023 AMC 12A #4, so both problems redirect to this page.

Problem

How many digits are in the base-ten representation of $8^5 \cdot 5^{10} \cdot 15^5$?

$\textbf{(A)}~14\qquad\textbf{(B)}~15\qquad\textbf{(C)}~16\qquad\textbf{(D)}~17\qquad\textbf{(E)}~18\qquad$

Solution 1

Prime factorizing this gives us $2^{15}\cdot3^{5}\cdot5^{15}=10^{15}\cdot3^5=243\cdot10^{15}$. $10^{15}$ gives us $15$ digits, and $243$ gives us $3$ digits. $15+3=\text{\boxed{\textbf{(E) }18}}$

~zhenghua


Video Solution by Math-X (First understand the problem!!!)

https://youtu.be/cMgngeSmFCY?si=b1khjbMn1i5rApCe&t=903

Video Solution

https://youtu.be/MFPSxqtguQo

~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)

Video Solution (Quick and Easy!)

https://youtu.be/Xy8vyymlPBg

~Education, the Study of Everything

See Also

2023 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 10 Problems and Solutions
2023 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 3
Followed by
Problem 5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 12 Problems and Solutions

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