In this task, you need to answer the given multiple-choice question on the general math. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.

Q: Problem: if a - b = 5 and a 2 + b 2 = 31 , find the value of ab . 
Options: a ) 9 , b ) 2 , c ) 3 , d ) 7 , e ) 12

A: c
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Q: Problem: village x has a population of 68000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ? 
Options: a ) 15 , b ) 19 , c ) 11 , d ) 18 , e ) 13

A: e
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Q: Problem: there are 20 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ? 
Options: a ) 10 , b ) 30 , c ) 190 , d ) 60 , e ) 90

A:
c
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