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Last year 26 members of a certain club traveled to England

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Last year 26 members of a certain club traveled to England

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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

OAB
You can find some solutions to this problem here: https://www.beatthegmat.com/official-guide-problem-t294129.html#788490

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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

OAB
Find the solution here https://www.beatthegmat.com/official-guide-problem-t294129.html#788509

Relevant book: Manhattan Review GMAT Sets & Statistics Guide

-Jay
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Hi Experts ,

Thanks for your reply.

Can you please advise that if question asks How many members of the club traveled to at least one of these three countries last year? So have we to find the total no. of students?

Please advise.

Thanks...

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rsarashi wrote:
Hi Experts ,

Thanks for your reply.

Can you please advise that if question asks How many members of the club traveled to at least one of these three countries last year? So have we to find the total no. of students?

Please advise.

Thanks...
That would be the case only if we knew that everyone in the club traveled to at least one of the three mentioned countries. But if the club could have contained members who didn't travel to any of the three mentioned countries, then we can't make this assumption.

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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

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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

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

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To England = 26
To France = 26
To Italy = 32

England and France = 0
England and Italy = 6
France and Italy = 11

All 3 = 0
Neither = 0

Total 26 + 26 + 32 -(0 + 6 + 11) + 0 + 0 = 67.

Regards!

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