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Out of a total of 85 children playing badminton or table tennis, the total number of girls in the group is 70% of the total number of boys in the group. The number of boys playing only badminton is 50% of the number of girls, and the total number of boys playing badminton is 60% of the total number of boys. The number of children playing only table tennis is 40% of the total number of children, and a total of 12 children play both badminton and table tennis. What is the number of girls playing only badminton?

1. 16
2. 14
3. 17
4. None of these

Correct answer: None of these

Solution

The data can be modeled using two overlapping sets: badminton and table tennis. Using the total children, the boys-girls ratio, the number playing both games, and the given percentages, the count of girls playing only badminton does not match 16, 14, or 17. Hence the correct option is 'None of these'.

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