Difference between revisions of "2019 AMC 10B Problems/Problem 14"
(→Solution) |
(→Solution) |
||
| Line 3: | Line 3: | ||
==Solution== | ==Solution== | ||
| − | We can figure out | + | We can figure out H = 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 T+M is congruent to 3 mod 9 and T-M is congruent to 7 mod 11. By inspection, we see that T = 4, M = 8 is a valid solution. Therefore the answer is 4+8+0 = 12. C |
- AZAZ12345 | - AZAZ12345 | ||
Revision as of 16:39, 14 February 2019
Problem
The base-ten representation for 
is 
, where 
, 
, and 
denote digits that are not given. What is 
?
Solution
We can figure out H = 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 T+M is congruent to 3 mod 9 and T-M is congruent to 7 mod 11. By inspection, we see that T = 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 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
