2001 AMC 10 Problems/Problem 12
Problem
Suppose that is the product of three consecutive integers and that is divisible by . Which of the following is not necessarily a divisor of ?
Solutions
Solution 1
Whenever is the product of three consecutive integers, is divisible by , meaning it is divisible by .
It also mentions that it is divisible by , so the number is definitely divisible by all the factors of .
In our answer choices, the one that is not a factor of is .
Solution 2
We can look for counterexamples. For example, letting , we see that is not divisible by 28, so is our answer.
See Also
2001 AMC 10 (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.