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Hard PS - looking for faster way to solve [#permalink]
01 Nov 2006, 18:10
100% (01:07) correct
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Took me 6 mins to solve this question manually, is there a faster way to solve it mathematically ?
In a class comprising boys and girls, there were 45 hand shakes amongst the girls and 105 hand shakes amongst the boys. How many hand shakes took place between a boy and a girl, if each member of the class shook hands exactly once with every other student in the class?
150 (Correct Answer)
Then the number of handshakes among girls is G choose 2 (I write GC2). So GC2 = 45. A useful thing to remember is that XC2 = X*(X-1)/2, so G = 10. Similarly, B = # boys so BC2 = 105 or B = 15. The # handshakes is then B*G = 150.
(Edit - I just saw that this is juaz' solution as well)