2024 AMC 8 Problem 4
Attempt Problem 4 of the 2024 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2024 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
4.
When Yunji added all the integers from to she mistakenly left out a number. Her incorrect sum turned out to be a square number. Which number did Yunji leave out?
Answer: E
Small hint:
The sum from to is
Big hint:
The incorrect sum must be a square below
Video solution:
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Written solution:
To find the number that Yunji left out, we need to find the sum of the integers from to and find its difference with the largest perfect square below the sum. We can calculate the sum of the integers from to as follows: The largest perfect square less than would be and .
Thus, E is the correct answer.
Problem 4 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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- 1989 AMC 8
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- 1991 AMC 8
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