2019 AMC 12A Problem 4

Below is the professionally curated solution for Problem 4 of the 2019 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2019 AMC 12A solutions, or check the answer key.

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Concepts:arithmetic sequencesymmetry

Difficulty rating: 1170

4.

What is the greatest number of consecutive integers whose sum is 45?45?

99

2525

4545

9090

120120

Solution:

Negative integers are allowed. The integers from 44-44 to 4444 sum to 0,0, so the integers from 44-44 to 4545 sum to 45.45.

This run has 45(44)+1=9045 - (-44) + 1 = 90 integers, and no longer run can work.

Thus, the correct answer is D.

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