Last year 26 members of a certain club traveled to England

rsarashi 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

OAB

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rsarashi 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 determine that 0 people traveled to all 3 countries because 0 people traveled to both England and France.

To determine how many people traveled to at least one country, we need to determine the total number of travelers. We can do this with the following formula:

At least one country = England + France + Italy - Sum of (Exactly two countries) - 2 times (All three countries)

At least one country = 26 + 26 + 32 - (6 + 11 + 0) - 2(0)

At least one country = 84 - 17 - 0 = 67

Answer: B

Hi All,

We're told that last year 26 members of a certain club traveled to England, 26 members traveled to France, and 32 members traveled to Italy and that 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.

This prompt is an example of a 3-group Overlapping Sets question - it's a rare question version that you probably will not see on Test Day. To solve it, you could set up a 3-circle Venn diagram or use the following formula:

Total = (Group 1) + (Group 2) + (Group 3) - (those in 1 and 2) - (those in 1 and 3) - (those in 2 and 3) - 2(those in all 3 groups).

Based on the data in the prompt, the equation would look like this:

Total = (26) + (26) + (32) - (0) - (6) - (11) - 2(0)
Total = 84 - 17
Total = 67

Final Answer: B

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Rich