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'.

Problem: the sum of all the integers k such that 25 < k < 24 is
Options: a ) 0 , b ) - 2 , c ) - 25 , d ) - 49 , e ) - 47
e

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
b

Problem: for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum of all the integers between 1 and 50 ?
Options: a ) 1275 , b ) 1542 , c ) 985 , d ) 1024 , e ) 1125
a