In a society it is customary for friends of the same sex to hug and for friends of opposite sex to shake hands when they meet. A group of friends met in a party and there were 24 handshakes. Which one among the following numbers indicates the possible number of hugs ?
- (a) 39
- (b) 30
- (c) 21 ✓ UPSC's answer
- (d) 20
Why the answer is (c)
• Let there be m men and w women. Handshakes happen only between a man and a woman, so m × w = 24.
• Hugs happen between two people of the same sex, so hugs = m(m − 1)/2 + w(w − 1)/2.
• Possible (m, w): (1, 24) gives 276 hugs; (2, 12) gives 67; (3, 8) gives 31; (4, 6) gives 6 + 15 = 21.
• Only 21 appears among the options — option (c).
• Hence option (c).
Why the other options are wrong
- (a) 39
- No split of the group with m × w = 24 gives 39 hugs.
- (b) 30
- No split of the group with m × w = 24 gives 30 hugs.
- (d) 20
- No split of the group with m × w = 24 gives 20 hugs.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2015, held on 23 August 2015. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.