2018 UNCO Math Contest II Problems/Problem 7
Problem
Let where and are randomly chosen with replacement from among the positive integers less than or equal to twelve. What is the probability that is a multiple of ?
Solution
To have a number divisible by , it must be divisible by and .
Consider mod 3 of x:
Here, since for A is even and odd respectively
is odd
Consider mod 4 of x:
we know A is odd, for , taking gives as result; for , taking gives as result, so we split the case for and here.
For ,
For ,
Concluding our above conditions, we have or
By counting the number of solutions, the required probability
See also
2018 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
All UNCO Math Contest Problems and Solutions |