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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 is summarized as 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 the three countries?
  • a)
    0
  • b)
    1
  • c)
    2
  • d)
    3
  • e)
    4
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A survey was conducted among a group of 83 American travel enthusiasts...
Given:
  • Total surveyed people = 83
  • Data about their visits to 3 countries is provided: Australia (referred to as A in the solution), Belgium (B) and Chile (C)
To find: The number of surveyed people who visited all 3 countries.
Approach:
  1. Let the number of surveyed people who visited all 3 countries be x
  2. Now, since this is a question that involves 3 sets (A, B and C), the most efficient way to solve it will be Venn Diagram. So, we’ll represent the given information in a Venn Diagram. Since x is the only unknown quantity in this question, we’ll be able to get a linear equation in x and so, get a unique value of x.
 
Working Out:
 
  • Since total number of people is 83, we can write:
    • {(28+x) +(8-x) +x+(4-x)} + {(10+x) + (12-x)} + (4+x) + 14 = 83
  • So, 40 + 40 + x = 83
  • 80 + x = 83
  • Therefore, x = 3
 
Looking at the answer choices, we see that the correct answer is Option D
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Most Upvoted Answer
A survey was conducted among a group of 83 American travel enthusiasts...
Given Information:
- 83 American travel enthusiasts were surveyed.
- 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.

Analysis:
To determine the number of surveyed travel enthusiasts who had visited all three countries (Australia, Belgium, and Chile), we need to find the intersection of the three sets: Australia visitors, Belgium visitors, and Chile visitors.

Let's use a Venn diagram to represent the given information:

```
A B C
/ \ / \ / \
AB AC BC / \ / \ /
| | | / \ / | /
| | | / \ | /
\ | | / \ |/
\ | |/ \ /
\ | / \ /
\ | / /
ABC
```

We are given the following information:
- A = 40 (visited Australia)
- B = 30 (visited Belgium)
- C = 20 (visited Chile)
- AB = 8 (visited Australia and Belgium)
- AC = 4 (visited Australia and Chile)
- BC = 12 (visited Belgium and Chile)
- None of the three countries = 14

Solution:
To find the number of surveyed travel enthusiasts who had visited all three countries, we need to find the value of ABC (the intersection of A, B, and C).

We can use the formula:
ABC = A + B + C - (AB + AC + BC) + None of the three countries

Substituting the given values:
ABC = 40 + 30 + 20 - (8 + 4 + 12) + 14
ABC = 104 - 24 + 14
ABC = 94 + 14
ABC = 108

Therefore, the number of surveyed travel enthusiasts who had visited all three countries is 108. However, since the total number of surveyed travel enthusiasts is 83, this is not possible.

Hence, the correct answer is option D) 3.
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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 is summarized as 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 countriesWhat is the number of surveyed travel enthusiasts who had visited all the three countries?a)0b)1c)2d)3e)4Correct answer is option 'D'. Can you explain this answer?
Question Description
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