Question

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 (d) 20

Answer 1

(c) Let x be the number of women.

Let y be the number of men.

Total number of hand shakes = xy = 24

Then, the possible factors of x and y are x = 6 or 4, 

y = 4 or 6