book Maths Puzzle Numerical Ability

Every man on earth has made a certain number of handshakes.Prove that the number of people who have made an odd number of handshakes is even.

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Pump A can fill a tank in 6 hours. Pump A and B together can fill the same tank in 3.5 hours. How long will it take to pump B to fill the tank alone? Can you show me how to do this problem? Thank you. please help me cause i forgot how to solve this problem. i will apreciate.

points A, B, and C are on circle P (P is the center of the circle). But points
A, P, and B measure