Printable

2020 AMC 10A Problem 22

Include the solution Back to the problem

2020 AMC 10A Problem 22AMC 10 Step by Step

Name: Date: September 13, 2026

Number Properties · difficulty 4 of 5 · about 6 min · position P21-25

For how many positive integers $n \le 1000$ is $\left\lfloor \dfrac{998}{n} \right\rfloor+\left\lfloor \dfrac{999}{n} \right\rfloor+\left\lfloor \dfrac{1000}{n}\right \rfloor$ not divisible by $3$ ? (Recall that $\lfloor x \rfloor$ is the greatest integer less than or equal to $x$ .)

A)
$22$
B)
$23$
C)
$24$
D)
$25$
E)
$26$

2020 AMC 10A Problem 22

Working