2003 AMC 10A Problems/Problem 20
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
The smallest base-11 number that has 3 digits in base-10 is which is .
The largest number in base-9 that has 3 digits in base-10 is Alternatively, you can do
The smallest number in base-9 that has 3 digits in base-10 is
Hence, all numbers that will have 3 digits in base-9, 10, and 11 will be between and , thus the total amount of numbers that will have 3 digits in base-9, 10, and 11 is
There are 900 possible 3 digit numbers in base 10.
Hence, the answer is
Video Solution by OmegaLearn
https://youtu.be/SCGzEOOICr4?t=596
~ pi_is_3.14
Video Solution
~IceMatrix
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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