🔥 New! 2025 AMC 10 B

Complete problem set with solutions and individual problem pages

Problem 2 Easy

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

  • A.

    9025

  • B.

    9070

  • C.

    9090

  • D.

    9115

  • E.

    9160

Answer:D
Solution

(10a + b)^2 = 100a^2 + 20ab + b^2 \equiv b^2 \pmod{10}, \quad a, b \in \mathbb{Z}

Let f(n) be the ones digit of n, then f(10a+b) = f(b).

\sum_{n=1}^{2025} f(n) = 202 \cdot \sum_{n=1}^{10} f(n) + \sum_{n=1}^{5} f(n) which is 202 \times (1+4+9+6+5+6+9+4+1+0) + (1+4+9+6+5) = 202 \times 45 + 25 = 9115.

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