1959 AMC 12 Problem 50
Attempt Problem 50 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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50.
A club with members is organized into four committees in accordance with these two rules:
Each member belongs to two and only two committees.
Each pair of committees has one and only one member in common.
Then
cannot be determined
has a single value between and
has two values between and
has a single value between and
has two values between and
Answer: D
Small hint:
Associate each member with the pair of committees to which that member belongs
Big hint:
Rule says every pair of the four committees occurs exactly once
Solution:
Each member belongs to exactly one unordered pair of committees. Conversely, each pair of committees has exactly one common member. Thus the members are in one-to-one correspondence with the pairs of four committees, so This is a single value between and
Therefore, the correct answer is D.