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Making committees

Source: 1959 AHSME Problem 50

August 14, 2013
AMC

Problem Statement

A club with xx members is organized into four committees in accordance with these two rules: (1) Each member belongs to two and only two committees \text{(1)}\ \text{Each member belongs to two and only two committees}\qquad (2) Each pair of committees has one and only one member in common\text{(2)}\ \text{Each pair of committees has one and only one member in common} Then xx: <spanclass=′latex−bold′>(A)</span> cannont be determined<span class='latex-bold'>(A)</span> \ \text{cannont be determined} \qquad <spanclass=′latex−bold′>(B)</span> has a single value between 8 and 16<span class='latex-bold'>(B)</span> \ \text{has a single value between 8 and 16} \qquad <spanclass=′latex−bold′>(C)</span> has two values between 8 and 16<span class='latex-bold'>(C)</span> \ \text{has two values between 8 and 16} \qquad <spanclass=′latex−bold′>(D)</span> has a single value between 4 and 8<span class='latex-bold'>(D)</span> \ \text{has a single value between 4 and 8} \qquad <spanclass=′latex−bold′>(E)</span> has two values between 4 and 8<span class='latex-bold'>(E)</span> \ \text{has two values between 4 and 8} \qquad
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