2019 AMC 10B Problems/Problem 14
Problem
The base-ten representation for 
is 
, where 
, 
, and 
denote digits that are not given. What is 
?
Solution
We can figure out T = 0 by noticing that 19! will end with 3 zeroes, as there are three 5's in its prime factorization. Next we use the fact that 19! is a multiple of both 11 and 9. sing their divisibility rules gives us that H+M is congruent to 3 mod 9 and H-M is congruent to 7 mod 11. By inspection, we see that H = 4, M = 8 is a valid solution. Therefore the answer is 4+8+0 = 12. C
- AZAZ12345
See Also
| 2019 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
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| All AMC 10 Problems and Solutions | ||
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