A group of market women sell at least one of yam, plantain and maize. 12 of them sell maize, 10 sell yam and 14 sell plantain. 5 sell plantain and maize, 4 sell yam and maize, 2 sell yam and plantain only while 3 sell all the three items. How many women are in the group?

  • A 25
  • B 19
  • C 18
  • D 17

The correct answer is A. 25

Let’s solve this problem using a Venn diagram. We can start by filling in the innermost value first, which is the number of women who sell all three items: yam, plantain, and maize. According to the problem, this value is 3.

Next, we can fill in the values for the intersections of two sets. The problem states that 5 women sell plantain and maize, but we have to subtract the 3 women who sell all three items to avoid counting them twice. So, the number of women who sell only plantain and maize is 5 - 3 = 2. Similarly, the number of women who sell only yam and maize is 4 - 3 = 1, and the number of women who sell only yam and plantain is given as 2.

Now we can fill in the values for each individual set. The problem states that 12 women sell maize, but we have to subtract the women who were already counted in the intersections to avoid counting them twice. So, the number of women who sell only maize is 12 - 2 - 1 - 3 = 6. Similarly, the number of women who sell only yam is 10 - 1 - 2 - 3 = 4, and the number of women who sell only plantain is 14 - 2 - 2 - 3 = 7.

Finally, we can add up all the values in the Venn diagram to find the total number of women in the group: 6 + 4 + 7 + 2 + 1 + 2 + 3 = 25.

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