At a party, Gerald saw Kathy standing alone at a punch bowl.

1. There were nineteen people altogether at the party who belonged to one of the three groups: unattached, engaged or married.
2. Each of seven people came alone; each of the rest came with a member of the opposite sex.
3. The couples who came to the party were either engaged to each other or married to each other.
4. The women who came alone were unattached.
5. No man who came alone was engaged.
6. The number of engaged men present equaled the number of married men present.
7. The number of married men who came alone equaled the number of unattached men who came alone.
8. Of the married women, engaged women, and unattached women present, Kathy belonged to the largest group.
9. 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