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: what is the greatest value of positive integer x such that 2 ^ x is a factor of 100 ^ 50 ? 
Options: a ) 70 , b ) 80 , c ) 90 , d ) 100 , e ) 120

Answer: d


Question: Problem: village p ’ s population is 1200 greater than village q ' s population . if village q ’ s population were reduced by 800 people , then village p ’ s population would be 6 times as large as village q ' s population . what is village q ' s current population ? 
Options: a ) 1050 , b ) 1100 , c ) 1150 , d ) 1200 , e ) 1250

Answer: d


Question: Problem: a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 100 that a person who randomly guesses the answer to each question will be a winner ? 
Options: a ) 5 , b ) 10 , c ) 50 , d ) 100 , e ) 1000

Answer:
c