Jerry wrote down the ones digit of each of the first 2025 positive squares: 1, 4, 9, 6, 5, 6, …. What is the sum of all the numbers Jerry wrote down?

2025 AMC 12B Problem 2

Attempt Problem 2 of the 2025 AMC 12B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2025 AMC 12B solutions, or check the answer key.

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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

Sum one full block of

10,

multiply by the number of blocks, then add the leftover terms

The ones digits of

1^2, 2^2, \ldots, 10^2

are

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

which sum to

45.

The

2025

terms contain

202

full blocks (

2020

terms) plus

5

more with digits

1, 4, 9, 6, 5

summing to

25.

The total is

202 \cdot 45 + 25 = 9090 + 25

= 9115.

Thus, the correct answer is D.