Problem: Of students taking at least one subject the number taking Mathematics and English only equals the number taking Mathematics only. No student takes English only or History only, and six students take Mathematics and History, but no English. The number taking English and History only is five times the number taking all three subjects. If the number taking all three subjects is even and non-zero, the number taking English and Mathematics only is:
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let represent the number of students taking Mathematícs and English only. Let ( , even) represent the number of students taking all three subjects. From the given information we have, then, , that is, . Under the restrictions given in the problem, this equation is satisfied only by and