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'.
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Question: Problem: the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 42 years , was replaced by a new person . find the age of the new person ? 
Options: a ) 22 , b ) 18 , c ) 12 , d ) 88 , e ) 66

Answer: c


Question: Problem: village x has a population of 76000 , 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 ) 17 , c ) 11 , d ) 18 , e ) 13

Answer: b


Question: Problem: let n ~ be defined for all positive integers n as the remainder when ( n - 1 ) ! is divided by n . what is the value of 30 ~ ? 
Options: a ) 1 , b ) 0 , c ) 2 , d ) 8 , e ) 31

Answer:
b