AMC 8 Daily Practice - Calculation Tricks by Grouping

Complete problem set with solutions and individual problem pages

Problem 4 Easy

What is the value of 2025 - 2024 + 2023 - 2022 + 2021 - 2020 + 2019 - 2018 + \dots + 3 - 2 + 1?

  • A.

    1012

  • B.

    1013

  • C.

    1014

  • D.

    1015

  • E.

    1016

Answer:B

By observing the arithmetic sequence, we notice that the sum of every two consecutive numbers from left to right is 1.

Therefore, we can group the numbers in pairs. Since there are 2025 numbers in total, dividing them into groups of two yields: 2025 \div 2 = 1012 groups with a remainder of 1.

Thus, the original expression can be rewritten as: 2025 - 2024 + 2023 - 2022 + 2021 - 2020 + 2019 - 2018 + \dots + 3 - 2 + 1 = (2025 - 2024) + (2023 - 2022) + (2021 - 2020) + (2019 - 2018) + \dots + (3 - 2) + 1 = \underbrace{1 + 1 + 1 + \dots + 1}_{1012 \text{ terms}} + 1 = 1 \times 1012 + 1 = 1013

The final result is \boxed{1013}.