Re: Fresh Meat!!!
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18 Apr 2013, 22:04
4. 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:
A. 30 < x < 36
B. 30 < x < 37
C. 31 < x < 37
D. 31 < x < 38
E. 32 < x < 38
Since X lies at most 38 from the options,
Lets find the number of Perfect Squared below 40= 1,4,9,16,25,36
Lets find the number of Primes below 40= 2,3,5,7,11,13,17,19,23,29,31,37
Now, f(x) + g(x) = 16
Start with Option C: no of primes less than 31 = \(11\)
no of p.s less than 31: \(5\)
Total = 16
Answer: C
P.S: The reason I started with option C is because when I analyzed choice A, the value of x is not fixed, and moving the value of A can shift the value of f(x)+g(x). Hence, I started looking for option where I can fix the value of "X"i.e. no prime number exists in that option.