Word Math Problem

Question

A survey of 62 customers was taken at a bookstore regarding the types of books purchased. The survey found that 37 customers purchased mysteries​, 31 purchased science fiction​, 22 purchased romance novels​,17 purchased mysteries and science fiction​, 11 purchased mysteries and romance novels​, 8 purchased science

fiction and romance novels​, and 3 purchased all three types of books.

​a) How many of the customers surveyed purchased only science fiction?

​b) How many purchased mysteries and science fiction, but not romance novels​?

​c) How many purchased mysteries or science fiction​?

​d) How many purchased mysteries or science fiction​, but not romance novels​?

​e) How many purchased exactly two types of​ books?

Answer 1

Set = 62; M = 37; SF = 31; R = 22; M intersect SF = 17; M intersect R = 11; SF intersect R = 8; (M intersect SF) intersect R =3

A) 31 bought SF -((17 bought SF and M + 8 bought SF and R) -3 bought SF, M, and R) = 31-25+3= 9 bought only SF

B) M intersect SF - (M intersect SF) intersect R = 17 - 3 = 14

C) M U SF -M intersect SF = 37 + 31-17 =51

D) (M U SF) not intersect R = 51 - (M isect R + SF isect R - M isect SF isect R) = 51-11-8+3 = 35

E) (M isect SF) U (M isect R) U (SF isect R) not isect ((M isect SF) isect R) = 17+11+8-3 = 33

Check, 33 bought exactly 2 books from E, 3 bought 3 books, so 36 bought more than one book. so 26 bought only one book.

((M not isect SF) no isect R) U ((SF not isect M) not isect R) U ((R not isect M) not isect SF) = 37-(17+11-3) +31-(17+8-3)+22-(11+9-3) = 12+9+5 = 26 CHECKS

With only 62 customers, it might help to draw out dots for each book and draw venn diagrams.