f(3x+1) = 3f(x) + 1

[Brent@GMATPrepNow]

The function f(x) is such that f(3x+1) = 3f(x) + 1 for all values of x. If f(2)=5, then f(7)=
A) 13
B) 15
C) 16
D) 19
E) 22

Please note that this is not an official GMAT question; it’s my attempt to create difficult (650+ level) GMAT-style questions for this forum.

[DanaJ]

IMHO what you have to notice is that 7 = 3*2 + 1. So f(7) = 3f(2) + 1 = 3*5 + 1 = 16.

Answer: C.

[truplayer256]

I didn't really do it Dana's way but I kind of thought that f(x)=[f(3x+1)-1]/3, so I did f(2) and came up with f(2)=[f(7)-1]/3, we know that f(2)=5, so just solve for f(7)

5=[f(7)-1]/3
f(7)=16 C

[Brent@GMATPrepNow]

C it is - nice solutions.