Difference between revisions of "2011 AMC 8 Problems/Problem 15"
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<math> \textbf{(A) } 8 \qquad\textbf{(B) } 9 \qquad\textbf{(C) } 10 \qquad\textbf{(D) } 11 \qquad\textbf{(E) } 12 </math> | <math> \textbf{(A) } 8 \qquad\textbf{(B) } 9 \qquad\textbf{(C) } 10 \qquad\textbf{(D) } 11 \qquad\textbf{(E) } 12 </math> | ||
− | ==Video Solution== | + | ==Video Solution by OmegaLearn== |
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https://youtu.be/rQUwNC0gqdg?t=440 | https://youtu.be/rQUwNC0gqdg?t=440 | ||
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==Solution 2== | ==Solution 2== | ||
− | 4^5 has 4 digits while 5^10 has 7 digits. This means that 4^5 | + | <math>4^5</math> has <math>4</math> digits while <math>5^{10}</math> has <math>7</math> digits. This means that <math>4^5 \cdot 5^{10}</math> has a total of <math>7+4=\boxed{\textbf{(D)} 11}</math> digits. |
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+ | ==Video Solution 1 by SpreadTheMathLove== | ||
+ | https://www.youtube.com/watch?v=mYn6tNxrWBU | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2011|num-b=14|num-a=16}} | {{AMC8 box|year=2011|num-b=14|num-a=16}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Latest revision as of 15:09, 17 December 2023
Contents
Problem
How many digits are in the product ?
Video Solution by OmegaLearn
https://youtu.be/rQUwNC0gqdg?t=440
Solution
That is one followed by ten
's, which is
digits.
Solution 2
has
digits while
has
digits. This means that
has a total of
digits.
Video Solution 1 by SpreadTheMathLove
https://www.youtube.com/watch?v=mYn6tNxrWBU
See Also
2011 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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 AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.