What is the value of 9901 × 101 - 99 × 10101?

2024 AMC 10A Problem 1 — Solution

2024 AMC 10A Problem 1

Below is the professionally curated solution for Problem 1 of the 2024 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2024 AMC 10A solutions, or check the answer key.

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Concepts:whole number operations

Difficulty rating: 860

What is the value of $9901 \cdot 101 - 99 \cdot 10101?$

$2$

$20$

$21$

$200$

$2020$

Solution:

Just compute each piece. We have $9901 \cdot 101 = 990100 + 9901 = 1000001,$ and $99 \cdot 10101 = 999999.$ Subtracting, $1000001 - 999999 = 2.$ Thus, A is the correct answer.

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