1952 AMC 12 Problem 1
Attempt Problem 1 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).
1.
If the radius of a circle is a rational number, its area is given by a number which is:
Rational
Irrational
Integral
A perfect square
None of these
Answer: B
Small hint:
Write the area in terms of the radius and
Big hint:
A circle’s radius is positive, so its rational square is nonzero
Solution:
If the positive rational radius is then its area is The factor is a nonzero rational number, and a nonzero rational multiple of the irrational number is irrational.
Thus, the correct answer is B.
Problem 1 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
- 1957 AMC 12
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- 1959 AMC 12
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