Problem Solving

[GMAT math practice question]

The function f(x) is defined as follows
f(x)={x/5 , (n is a multiple of 5) x+1 , (n is not a multiple of 5)

Moreover, f(xn) = xn+1, and f(x1) = 1000. What is the value of f(x50)?

A. 1
B. 2
C. 3
D. 4
E. 5

=>

f(x1) = x2 = 1000
f(x2) = x3 = 1000/5 = 200
f(x3) = x4 = 200/5 = 40
f(x4) = x5 = 40/5 = 8
f(x5) = x6 = 8 + 1 = 9 (because 8 is not a multiple of 5)
f(x6) = x7 = 9 + 1 = 10
f(x7) = x8 = 10/5 = 2
f(x8) = x9 = 2 + 1 = 3
f(x9) = x10 = 3 + 1 = 4
f(x10) = x11 = 4 + 1 = 5
f(x11) = x12 = 5/5 = 1
f(x12) = x13 = 1 + 1 = 2
f(x13) = x14 = 2 + 1 = 3
f(x14) = x10 = 3 + 1 = 4
f(x15) = x11 = 4 + 1 = 5
…
f(x5k) = 5

Therefore, E is the answer.
Answer: E