2016 AMC 8 Problems/Problem 24
The digits , , , , and are each used once to write a five-digit number . The three-digit number is divisible by , the three-digit number is divisible by , and the three-digit number is divisible by . What is ?
Solution
We see that since is divisible by , must equal either or , but it cannot equal , so . We notice that since must be even, must be either or . However, when , we see that , which cannot happen because and are already used up; so . This gives , meaning . Now, we see that could be either or , but is not divisible by , but is. This means that and .
2016 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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