2001 AMC 10 竞赛试题/第11题
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 ?
Solution
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 (D) is our answer.
AEIS在线试听课程
