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Question
A group of people was traveling by bus. Six people spoke French, fifteen people spoke English, and six people spoke Spanish.
No other language was used by the people in that group. Two people in the group could speak both French and English, and one person could speak all three languages.
How many people were there in the group?
A group of people was traveling by bus. Six people spoke French, fifteen people spoke English, and six people spoke Spanish.
No other language was used by the people in that group. Two people in the group could speak both French and English, and one person could speak all three languages.
How many people were there in the group?
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Solution
The correct option is A 23
Total people who could speak:
French = 6
English = 15
Spanish = 6
Number of people who could speak both French and English = 2
Number of people who could speak all three languages = 1
Thus, the number of people who could only speak one language:
French = 6 – 2 – 1 = 3
English = 15 – 2 – 1 = 12
Spanish = 6 – 1 = 5
So,
Total number of people in the group = 3 + 2 + 1 + 12 + 5
= 23
Thus, there were 23 people in the group traveling by bus.
Total people who could speak:
French = 6
English = 15
Spanish = 6
Number of people who could speak both French and English = 2
Number of people who could speak all three languages = 1
Thus, the number of people who could only speak one language:
French = 6 – 2 – 1 = 3
English = 15 – 2 – 1 = 12
Spanish = 6 – 1 = 5
So,
Total number of people in the group = 3 + 2 + 1 + 12 + 5
= 23
Thus, there were 23 people in the group traveling by bus.
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