You are given a math word problem and you are supposed to make use of mathematical concepts like probability, combinatorics, linear equations, sequences/series, or simple operators like addition, subtraction, division, or multiplication to answer the given question. Choose the best option from the 5 given options and report that option.

Question: There are some pigeons and hares in a zoo. If heads are counted, there are 120. If legs are counted, there are 580. The number of hares in the zoo is?

 Option A: 20

 Option B: 82

 Option C: 190

 Option D: 137

 Option E: 170
Option E

Question: Machine P and Machine Q are each used to manufacture 770 sprockets. It takes Machine P 10 hours longer to produce 770 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce?

 Option A: 3

 Option B: 5

 Option C: 7

 Option D: 9

 Option E: 11
Option C

Question: 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 1/10 that a person who randomly guesses the answer to each question will be a winner?

 Option A: 5

 Option B: 10

 Option C: 50

 Option D: 100

 Option E: 1000

Option D