In a fraternity with 35 members, 18 take mathematics, 5 take both mathematics and art history, and 8 take neither mathematics nor art history. How many take art history but not mathematics?

Question

anonymous · Answer

The easiest way to solve this problem is by drawing a venn diagram. you know 18 take math, 5 take math and art, 8 take neither, and that there are 35 total people. if 18 take math and 5 of those 18 take art as well, 5 take both and 13 take only math. |dw:1393378486921:dw|

The total number of members = the number of members in art only + members in math only + members in both + members in neither.
Thus:
35=5+13+8+a
a=#of members in art only = 9