2003 AMC 10A Problems/Problem 20
Contents
Problem 20
A base-10 three digit number is selected at random. Which of the following is closest to the probability that the base-9 representation and the base-11 representation of are both three-digit numerals?
Solution
To be a three digit number in base-10:
Thus there are three-digit numbers in base-10
To be a three-digit number in base-9:
To be a three-digit number in base-11:
So,
Thus, there are base-10 three-digit numbers that are three digit numbers in base-9 and base-11.
Therefore the desired probability is .
Video Solution by OmegaLearn
https://youtu.be/SCGzEOOICr4?t=596
~ pi_is_3.14
Video Solution
~IceMatrix
Video Solution by WhyMath
~savannahsolver
See Also
2003 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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All AMC 10 Problems and Solutions |
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