3-set problems

Official Guide practice (find these in your Official Guide or at www.gmatclub.com) Solve these problems using the “card method”.

PS01987 Last year 26 members of a certain club traveled to England

PS04711 A certain experimental mathematics program was tried out

PS04677 Of the 300 subjects who participated in an experiment

PS07712 Of the 150 houses in a certain development

In a class of 33, 20 play cricket, 25 play football and 18 play hockey. 

There are 150 students at Seward High School. 66 students play baseball, 45 play basketball, and 42 play soccer. 

Each of 90 students participated in at least one of three track tryouts

Further tasks

This formula can be useful for solving 3 set problems. Take some time to interpret it using the ‘card method’:

Total # of elements = (# in A) + (# in B) + (# in C) – (# in exactly 2 sets) – 2  (# in exactly 3 sets) + (number in no set)

Go back to the Official Guide problems above and try to solve them using a Venn diagram and the 3-set formula. Which strategy works best for each problem?