At a party, Gerald saw Kathy standing alone at a punch bowl.
- There were nineteen people altogether at the party who belonged to one of the three groups: unattached, engaged or married.
- Each of seven people came alone; each of the rest came with a member of the opposite sex.
- The couples who came to the party were either engaged to each other or married to each other.
- The women who came alone were unattached.
- No man who came alone was engaged.
- The number of engaged men present equaled the number of married men present.
- The number of married men who came alone equaled the number of unattached men who came alone.
- Of the married women, engaged women, and unattached women present, Kathy belonged to the largest group.
- Gerald, who was unattached, wanted to know which group of women Kathy belonged to.
Which one of the three groups did Kathy belong to?
- Let Mau, Mam be men who came alone and were unattached and married resp.
- Let Mpm, and Mpe be men who came as couple who are married or engaged resp.
- Let Wau, Wpm,Wpe be women who came alone and unattached and women who came as pair who are married or engaged respectively
1) Mau+Mam+Wau=7 and 2) Mau=Mam ( i.e 1,2,3)
3) Mpe+Mpm=Wpe+Wpm=6 and 4) Mam+Mpm=Mpe
From 2), 3) and 4) Mau=Mam =2 so that sum of married and engaged is even
hence Wau =3, Wpm = 2 and Wpe =4
Hence Kathy belongs to Engaged group.
Posted by Salil
on 2014-02-07 01:41:44