2012 AIME I Problems/Problem 1
Problem 1
Find the number of positive integers with three not necessarily distinct digits, , with and such that both and are multiples of .
Solution
A positive integer is divisible by if and only if its last two digits are divisible by 4. For any value of , there are two possible values for and , since we find that if is even, and must be either or , and if is odd, and must be either or . Thus, there are ways to choose and , and ways to choose (since can be any digit). Therefore, the final answer is .
See also
2012 AIME I (Problems • Answer Key • Resources) | ||
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