In a group of market women, 12 sell maize, 10 sell yam, and 14 sell plantain. 5 sell plantain and maize, 4 sell yam and maize, and 2 sell only yam and plantain. If 3 sell all three items, how many women are in the group?

Question 461 of 480

In a group of market women, 12 sell maize, 10 sell yam, and 14 sell plantain. 5 sell plantain and maize, 4 sell yam and maize, and 2 sell only yam and plantain. If 3 sell all three items, how many women are in the group?

Correct Answer: A

Explanation

Using the principle of inclusion-exclusion for three sets: Total = (Yam + Plantain + Maize) - (Yam&Plantain + Yam&Maize + Plantain&Maize) + (All three). Substituting: Total = (10+14+12) - (2+4+5) + 3 = 36 - 11 + 3 = 28. However, careful region-based calculation from the problem yields 25. Let only Yam = a, only Plantain = b, only Maize = c. c = 12 - (those selling maize and others) = 12 - (5+4-3) = 6. a = 10 - (2+4-3) = 7. b = 14 - (2+5-3) = 10. Total = a+b+c+(Y&P only)+(Y&M only)+(P&M only)+All three = 7+10+6+2+1+2+3 = 25. (Y&M only = 4-3=1, P&M only = 5-3=2).