1955 AMC 12 Problem 38
Attempt Problem 38 of the 1955 AMC 12 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 1955 AMC 12 solutions, or check the answer key.
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38.
Four positive integers are given. Select any three of these integers, find their arithmetic average, and add this result to the fourth integer. Thus the numbers and are obtained. One of the original integers is:
Answer: B
Small hint:
If the original sum is and the singled-out integer is the result is
Big hint:
Sum all four reported results to determine
Solution:
If the original integers sum to the result associated with singled-out integer is Summing all four reported results counts the total as so The result therefore comes from
Thus, one original integer is and the correct answer is B.