In a group of 80 tourists, 36 visited Agra, 32 visited Jaipur and 30 visited Udaipur. 14 visited both Agra and Jaipur, 11 visited both Agra and Udaipur, 10 visited both Jaipur and Udaipur, and 5 visited all three cities (each ‘both’ count includes these 5). How many tourists visited exactly one of the three cities?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 43
The tourists who visited only one city are found circle by circle: from each city total take away the two ‘both’ counts of that city, and add back the 5 who visited all three, as they were taken away twice.
Agra only \(=36-14-11+5=16\)
Jaipur only \(=32-14-10+5=13\)
Udaipur only \(=30-11-10+5=14\)
Exactly one city \(=16+13+14=43\)
Checking the other options
Option (1): 20 — Incorrect. This is the number who visited exactly two of the cities.
Option (3): 28 — Incorrect. This takes the two ‘both’ counts from each city total but does not add back the 5 who visited all three, who were taken away twice.
Option (4): 68 — Incorrect. This is the number who visited at least one of the cities.