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At a meeting of 100 people, there were 23 Indian men and 29 Indian women. Of these Indians, 4 were dentists and 24 were either men or dentists. Assume that there were no foreign dentists. How many foreigners attended the meeting?  
  • a)
    45
  • b)
    46
  • c)
    47
  • d)
    48
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
At a meeting of 100 people, there were 23 Indian men and 29 Indian wom...
Understanding the Problem
To find the number of foreigners in a meeting of 100 people, we need to analyze the given information about the Indian attendees.
Information Breakdown
- Total attendees: 100 people
- Indian men: 23
- Indian women: 29
- Total Indians: 23 + 29 = 52
Calculating Dentists and Overlap
- Indian dentists: 4
- Indians who are either men or dentists: 24
This tells us that the overlap of men and dentists among Indians needs to be carefully considered.
Identifying Indian Men who are Dentists
Since there are 4 Indian dentists and the total number of Indians who are either men or dentists is 24, we can set up the equation:
- Total Indian men: 23
- Total Indian dentists: 4
Using the principle of inclusion-exclusion:
- Indian men who are not dentists: 23 - x
- Indian dentists who are men: x (where x is the number of Indian dentists who are men)
The equation can be simplified to find the value of x.
Solving for Foreigners
Now, let's analyze the numbers:
- Total Indians (52) include 4 dentists, meaning 48 are not dentists.
- Since there are 24 who are either men or dentists, overlapping those gives us 24 - 4 = 20 Indians who are either men or not dentists.
Now we can find the number of foreigners:
- Total people: 100
- Total Indians: 52
So, the number of foreigners is:
100 - 52 = 48
Conclusion
Thus, the number of foreigners who attended the meeting is:
48 (Correct answer is option 'D').
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