2025 AMC 10B Problem 2

Question

Jerry wrote down the ones digit of each of the first

2025

positive squares:

1,

4,

9,

6,

5,

6,

\ldots

What is the sum of all the numbers Jerry wrote down?

9025

9070

9090

9115

9160

The ones digit of

n^2

depends only on the ones digit of

n,

so the list repeats every

10

terms

One full block

1, 4, 9, 6, 5, 6, 9, 4, 1, 0

sums to

45;

there are

202

full blocks and

5

leftover terms

The ones digit of

n^2

depends only on the ones digit of

n,

so the list repeats every

10

terms:

1, 4, 9, 6, 5, 6, 9, 4, 1, 0.

One block sums to

45.

Now

2025 = 202 \cdot 10 + 5,

so we get

202

full blocks plus the first five terms:

202 \cdot 45

+ (1 + 4 + 9 + 6 + 5)

= 9090

+ 25 = 9115.

Therefore, the answer is D.

Problem 2 in other years