2024 AMC 12B Problem 1

Attempt Problem 1 of the 2024 AMC 12B 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 2024 AMC 12B solutions, or check the answer key.

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

1.

In a long line of people arranged left to right, the 10131013th person from the left is also the 10101010th person from the right. How many people are in the line?
20212021
20222022
20232023
20242024
20252025
Answer: B
Concepts:counting integers in a rangebasic counting
Small hint:
The people to the left of the target person and the people to the right, plus the person themself, make up the whole line
Big hint:
There are 10121012 people to the left and 10091009 to the right; add these to the target person
Solution:
The target person has 1013−1=10121013 - 1 = 1012 people to the left and 1010−1=10091010 - 1 = 1009 people to the right. Including the person themself, the line has 1012+1009+1=20221012 + 1009 + 1 = 2022 people.
Thus, the correct answer is B.
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