1959 AMC 12 Problem 46
Attempt Problem 46 of the 1959 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 1959 AMC 12 solutions, or check the answer key.
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46.
A student on vacation for days observed that
it rained times, morning or afternoon;
when it rained in the afternoon, it was clear in the morning;
there were five clear afternoons;
there were six clear mornings.
Then equals:
Answer: B
Small hint:
Count rainy mornings and rainy afternoons from the numbers of clear half-days
Big hint:
Condition ensures that a rainy afternoon and rainy morning never occur on the same day
Solution:
There are rainy mornings and rainy afternoons. By condition these are distinct rainy occasions, and their total is Hence so and
Thus, the correct answer is B.