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:  Select:
A) 30 < x < 36  B) 30 < x < 37  C) 31 < x < 37  D) 31 < x < 38  E) 32 < x < 38
f(n) = number of perfect squares less than n   1,4,9,16,25,36   f(25) = 4   f(26)=f(27)=...=f(35)=f(36) = 5   f(37) = 6   g(n) = number of prime numbers less than n   2,3,5,7,11,13,17,19,23,29,31,37   g(31)=10   g(32)=g(33)=...=g(36)=g(37) = 11   g(38)=12   f(x)+g(x)=16 implies that f(x)=5 and g(x)=11.   So, x = 32,33,34,35,or36.   Answer 31 &lt; x &lt; 37, 31 &lt; x &lt; 37.
<result>C</result>
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: