2021 AMC 12B Fall Problem 1

Attempt Problem 1 of the 2021 AMC 12B Fall 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 2021 AMC 12B Fall solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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

$10{,}000$

$10{,}010$

$10{,}110$

$11{,}000$

$11{,}110$

Answer: E

Concepts:place value symmetry

Difficulty rating: 720

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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