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.
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Question: Question: If the average (arithmetic mean) of 18 consecutive odd integers is 414, then the least of these integers is

 Option A: a

 Option B: b

 Option C: c

 Option D: d

 Option E: e

Answer: Option A


Question: Question: In an electric circuit, two resistors with resistances x and y are connected in parallel. If R is the combined resistance of these two resistors, then the reciprocal of R is equal to the sum of the reciprocals of x and y. What is R if x is 5 Ohms and y is 7 Ohms?

 Option A: 3/5

 Option B: 1/7

 Option C: 12/35

 Option D: 31/12

 Option E: 35/12

Answer: Option E


Question: Question: When positive integer n is divided by 3, the remainder is 1. When n is divided by 11, the remainder is 9. What is the smallest positive integer k such that k+n is a multiple of 33?

 Option A: 2

 Option B: 4

 Option C: 6

 Option D: 8

 Option E: 10

Answer:
Option A