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 average of 13 numbers is 60 . average of the first 7 of them is 57 and that of the last 7 is 61 . find the 8 th number ? 
Options: a ) 43 , b ) 30 , c ) 35 , d ) 45 , e ) 50
a

Problem: the “ a - number ” of a number x is defined as the ones digit of 2 ^ x . antony rolls a die with 6 sides labeled with the integers from 1 to 6 , each of which has an equal probability of landing face - up . he then takes 3 ^ a , where a is the a - number of the result of his die roll , and plots 3 ^ a on a number line as the point a . finally , he repeats this entire process , this time plotting the result as the point b . what is the probability that the distance between a and b is greater than the value of b ? 
Options: a ) 3 / 8 , b ) 13 / 36 , c ) 17 / 36 , d ) 19 / 36 , e ) 23 / 36
b

Problem: divide rs . 1300 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ? 
Options: a ) 346 , b ) 368 , c ) 375 , d ) 337 , e ) 325

e