2023 AMC 10A Problem 3

Problem 3 of 25EasierNumber Theory

How many positive perfect squares less than

2023

are divisible by

5?

Show solution

Solution

If a perfect square is divisible by

5,

it’s divisible by

25,

so it looks like

(5k)^2 = 25k^2.

We need

25k^2 \lt 2023,

i.e.

k^2 \lt 80.9.

That allows

k = 1, 2, \ldots, 8,

which is

8

squares. Thus, A is the correct answer.

Concepts: perfect square · divisibility

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.