2021 AMC 12B Fall Problem 1

Below is the professionally curated solution for Problem 1 of the 2021 AMC 12B Fall, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2021 AMC 12B Fall solutions, or check the answer key.

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Concepts:place value symmetry

Difficulty rating: 720

What is the value of $1234 + 2341 + 3412 + 4123?$

$10{,}000$

$10{,}010$

$10{,}110$

$11{,}000$

$11{,}110$

Solution:

Each of the digits $1, 2, 3, 4$ appears exactly once in the thousands, hundreds, tens, and units columns. So each column sums to $1 + 2 + 3 + 4 = 10.$

The total is therefore $10 \cdot 1111 = 11110.$

Thus, the correct answer is E.

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