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 
by noticing that will end with 
zeroes, as there are three 
's in its prime factorization. Next we use the fact that is a multiple of both 
and 
. Since their divisibility rules gives us that 
is congruent to mod and that 
is congruent to 
mod . By inspection, we see that 
is a valid solution. Therefore the answer is 
, which is (C).
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 | ||
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