instruction:
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'.
question:
Problem: for any integer k greater than 1 , the symbol k * denotes the product of all integers between 1 and k , inclusive . if k * is a multiple of 1701 what is the least possible value of k ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
answer:
c

question:
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
answer:
e

question:
Problem: if 50 % of a number is equal to one - third of another number , what is the ratio of first number to the second number ?
Options: a ) 2 : 5 , b ) 1 : 4 , c ) 3 : 7 , d ) 6 : 11 , e ) 2 : 3
answer:
e