2021 AMC 10B Problems/Problem 1
Contents
[hide]Problem
How many integer values of satisfy ?
Solution
Since is about , we multiply 9 by 2 and add 1 to get ~smarty101
Solution 2
There are two cases here.
When and So then
When and So then . Dividing by and flipping the sign, we get
From case 1 and 2, we need . Since is an integer, we must have between and . There are a total of
-PureSwag
Solution 3
. Since is approximately , is approximately . We are trying to solve for , where . Hence, , for . The number of integer values of is . Therefore, the answer is .
~ {TSun} ~