A survey was conducted among a group of 83 American travel enthusiasts to determine the countries that the group members

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Sun Dec 27, 2020 3:29 pm

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A survey was conducted among a group of 83 American travel enthusiasts to determine the countries that the group members had visited. The data collected in the survey are summarized below:

40 had visited Australia
30 had visited Belgium
20 had visited Chile
8 had visited Australia and Belgium
12 had visited Belgium and Chile
4 had visited Australia and Chile
14 had visited none of the three countries

What is the number of surveyed travel enthusiasts who had visited all three countries?

A. 0
B. 1
C. 2
D. 3
E. 4

Answer: D

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Source: Beat The GMAT — Problem Solving | Sun Dec 27, 2020 3:29 pm

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Re: A survey was conducted among a group of 83 American travel enthusiasts to determine the countries that the group mem

by Scott@TargetTestPrep » Mon Mar 22, 2021 8:36 am

M7MBA wrote: ↑
Sun Dec 27, 2020 3:29 pm
A survey was conducted among a group of 83 American travel enthusiasts to determine the countries that the group members had visited. The data collected in the survey are summarized below:

40 had visited Australia
30 had visited Belgium
20 had visited Chile
8 had visited Australia and Belgium
12 had visited Belgium and Chile
4 had visited Australia and Chile
14 had visited none of the three countries

What is the number of surveyed travel enthusiasts who had visited all three countries?

A. 0
B. 1
C. 2
D. 3
E. 4

Answer: D

Solution:

Let A be Australia, B be Belgium and C be Chile. We can use the formula:

Total = N(A) + N(B) + N(C) - N(A & B) - N(A & C) - N(B & C) + N(A & B & C) + N(None)

83 = 40 + 30 + 20 - 8 - 12 - 4 + n + 14

83 = 80 + n

3 = n

Answer: D

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