Question Detail
Question
In a sample of 1000 foodstuffs scores taken at a market, 200 stock rice, 240 stock beans, 250 stock flour, 64 both beans and rice, 97 both rice and flour, while 60 stock beans and flour. If 430 do not stock any, how many stock all?
Correct Answer
Option B is the correct answer.
Detailed Explanation
Let R, B, F be sets for rice, beans, flour. Total = 1000, none = 430, so at least one = 570. Using inclusion-exclusion: |R∪B∪F| = |R| + |B| + |F| - |R∩B| - |R∩F| - |B∩F| + |R∩B∩F|. 570 = 200 + 240 + 250 - 64 - 97 - 60 + x → 570 = 690 - 221 + x → 570 = 469 + x → x = 570 - 469 = 101. Wait, 690 - 221 = 469, so 570 = 469 + x → x = 101. But option B is 101. However, check if any overlap counted incorrectly: 64 both beans and rice includes those with all three, similarly for others. So x = 101 seems correct.
Hint
Use the principle of inclusion-exclusion for three sets.