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In a school, 21 students are in the cricket team, 26 in the hockey team, and 29 in the football team. Among them, 14 play both hockey and cricket, 15 play both hockey and football, and 12 play both football and cricket. Eight students play all three games. If k is the total number of members across the three athletic teams, find the sum of digits of k.

1. 6
2. 7
3. 8
4. 9

Correct answer: 7

Solution

Using the principle of inclusion-exclusion: k = |C| + |H| + |F| - |C∩H| - |H∩F| - |C∩F| + |C∩H∩F| = 21 + 26 + 29 - 14 - 15 - 12 + 8 = 76 - 41 + 8 = 43. Sum of digits of 43 = 4 + 3 = 7.

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