Problem Solving

Hi All,

Last year 26 members of a certain club traveled to England, 26 members traveled to France, and 32 members traveled to Italy. Last year no members of the club traveled to both England and France, 6 members traveled to both England and Italy, and 11 members traveled to both France and Italy. We're asked for the number of members of the club who traveled to at least one of these three countries last year. In simpler terms, we're asked for the total number of members in the club. While the prompt does not explicitly state it, we're meant to assume that none of the members traveled to all 3 countries last year.

3-Group Overlapping Sets questions are relatively rare on the Official GMAT (you likely will NOT see this version of Overlapping Sets on Test Day). However, there is a formula that you can use to solve it.

Total = (1st group) + (2nd group) + (3rd group) - (1st and 2nd) - (1st and 3rd) - (2nd and 3rd) - 2(all 3 groups).

In overlapping sets questions, any person who appears in more than one group has been counted more than once. When dealing with groups of people, you're not supposed to count any individual more than once, so the formula 'subtracts' all of the extra times that a person is counted. For example, someone who is in BOTH the 1st group and the 2nd group will be counted twice....that's why we SUBTRACT that person later on [in the (1st and 2nd) group].

In this prompt, we're given a number for each of the 3 individual groups and the number of people who appear in each of the '2 group combinations.' The equation would look like this...

Total = 26 + 26 + 32 - (1st and 2nd) - (1st and 3rd) - (2nd and 3rd) - 2(0)

Total = 26 + 26 + 32 - (0) - (6) - (11) - 2(0)

Total = 84 - 17 = 67

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

swerve wrote:Last year 26 members of a certain club traveled to England, 26 members traveled to France, and 32 members traveled to Italy. Last year no members of the club traveled to both England and France, 6 members traveled to both England and Italy, and 11 members traveled to both France and Italy. How many members of the club traveled to at least one of these three countries last year?

A. 52
B. 67
C. 71
D. 73
E. 79

We are given the following:

England travelers = 26

France travelers = 26

Italy travelers = 32

England and France travelers = 0

England and Italy travelers = 6

France and Italy travelers = 11

Although it's not stated directly, we can infer that 0 people traveled to all 3 countries because 0 people traveled to both England and France.

In determining how many people traveled to at least one country, we are actually determining the total number of travelers, since each traveler did travel to at least one country. We can do this with the following formula:

Total travelers = England + France + Italy - sum of (exactly two countries) - 2 times (all three countries)

Total travelers = 26 + 26 + 32 - (6 + 11 + 0) - 2(0)

Total travelers = 84 - 17 - 0 = 67

Thus, 67 people traveled to at least one country.

Answer: B