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JAMB 1999 · UME · Q9

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 three items. How many women are in the group?

Worked solution (try it first)
  1. Fill the Venn diagram from the centre out.
  2. All three: 3.
  3. Yam and plantain only: 2.
  4. Plantain and maize only: 5−3=25 - 3 = 2.
  5. Yam and maize only: 4−3=14 - 3 = 1.
  6. Maize only: 12−3−2−1=612 - 3 - 2 - 1 = 6.
  7. Yam only: 10−3−1−2=410 - 3 - 1 - 2 = 4.
  8. Plantain only: 14−3−2−2=714 - 3 - 2 - 2 = 7.
  9. Add all seven regions: 3+2+2+1+6+4+7=253 + 2 + 2 + 1 + 6 + 4 + 7 = 25, option A.

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