1952 AMC 12 Problem 31
Attempt Problem 31 of the 1952 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 1952 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
31.
Given points in a plane no three of which are collinear, the number of lines they determine is:
None of these
Answer: D
Small Hint:
Each line is determined by choosing two of the points
Big Hint:
The condition that no three are collinear ensures that different pairs determine different lines
Solution:
Every pair of points determines one line, and no line is counted by more than one pair because no three points are collinear. Therefore the number of lines is
Thus, the correct answer is D.
Problem 31 in Other Years
1950 AMC 12 · 1951 AMC 12 · 1953 AMC 12 · 1954 AMC 12 · 1955 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