instruction:
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:
Question: The functions f and g are defined for all the positive integers n by the following rule: f(n) is the number of perfect squares less than n and g(n) is the number of primes numbers less than n. If f(x) + g(x) = 16, then x is in the range:

 Option A: 30 < x < 36

 Option B: 30 < x < 37

 Option C: 31 < x < 37

 Option D: 31 < x < 38

 Option E: 32 < x < 38
answer:
Option C


question:
Question: A candidate got 32% of the votes polled and he lost to his rival by 1908 votes. How many votes were cast?

 Option A: 5100

 Option B: 5200

 Option C: 5300

 Option D: 5400

 Option E: 5500
answer:
Option C


question:
Question: 11 persons are sitting ina row. how many ways can 11persons be arranged in a row such that 3 persons should always be together?

 Option A: 7!×3!

 Option B: 7!×2!

 Option C: 9!×3!

 Option D: 7!×1!

 Option E: 6!×2!
answer:

Option C