TASK DEFINITION: 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: 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

SOLUTION: c

PROBLEM: Problem: a ’ s speed is 20 / 19 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ? 
Options: a ) 1 / 19 , b ) 3 / 19 , c ) 1 / 10 , d ) 1 / 20 , e ) 3 / 10

SOLUTION: d

PROBLEM: Problem: an assembly line produces 90 cogs per hour until an initial order of 60 cogs is completed . the speed of the assembly line is then immediately decreased so that it only produces 60 cogs per hour until another 60 cogs are produced . what is the overall average output , in cogs per hour , for the assembly line during this whole time ? 
Options: a ) 68 , b ) 69 , c ) 70 , d ) 71 , e ) 72

SOLUTION:
e