Problem:
At a math contest, 57 students are wearing blue shirts, and another 75 students are wearing yellow shirts. The 132 students are assigned into 66 points. In exactly 23 of these pairs, both students are wearing blue shirts. In how many pairs are both students wearing yellow shirts?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Answer (B): There are 46 blue-shirted students in the all-blue pairs. Thus blue-shirted students are paired with yellow-shirted students, leaving yellow-shirted students in all-yellow pairs. Hence there are all-yellow pairs.
The problems on this page are the property of the MAA's American Mathematics Competitions