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 — Solution

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?

$9025$

$9070$

$9090$

$9115$

$9160$

Answer: D

Concepts:units digit pattern recognition summation

Difficulty rating: 1020

Solution:

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.

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