2008 AMC 8 Problems/Problem 22
Contents
[hide]Problem
For how many positive integer values of are both and three-digit whole numbers?
Solution
If is a three-digit whole number, must be divisible by 3 and be . If is three digits, n must be So it must be divisible by three and between 300 and 333. There are such numbers, which you can find by direct counting.
Solution 2
Instead of finding n, we find . We want and to be three-digit whole numbers. The smallest three-digit whole number is , so that is our minimum value for , since if , then . The largest three-digit whole number divisible by is , so our maximum value for is . There are whole numbers in the closed set , so the answer is .
- ColtsFan10
See Also
2008 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
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All AJHSME/AMC 8 Problems and Solutions |
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