1955 AMC 12 Problem 35
Attempt Problem 35 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.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
35.
Three boys agree to divide a bag of marbles in the following manner. The first boy takes one more than half the marbles. The second takes a third of the number remaining. The third boy finds that he is left with twice as many marbles as the second boy. The original number of marbles:
is none of the following
cannot be determined from the given data
is or
is or
is or
Answer: B
Small Hint:
Let the original number be and express the remainder after the first boy
Big Hint:
Translate the last two boys’ share condition into an equation and see whether it determines uniquely
Solution:
The first boy takes leaving The second takes one third of that remainder, and the third receives the other two thirds, automatically twice the second boy’s share. Thus the share condition imposes no unique value of It only requires to be a nonnegative multiple of so many values such as work.
Therefore the original number cannot be determined, and the correct answer is B.
Problem 35 in Other Years
1950 AMC 12 · 1951 AMC 12 · 1952 AMC 12 · 1953 AMC 12 · 1954 AMC 12 · 1956 AMC 12 · 1957 AMC 12 · 1958 AMC 12 · 1959 AMC 12 · 1960 AMC 12 · 1961 AMC 12 · 1962 AMC 12 · 1963 AMC 12 · 1964 AMC 12 · 1965 AMC 12 · 1966 AMC 12 · 1967 AMC 12 · 1968 AMC 12 · 1969 AMC 12 · 1970 AMC 12 · 1971 AMC 12 · 1972 AMC 12 · 1973 AMC 12