Carcass wrote:
Let f be a function such that f(mn) = f(m)f(n) for every positive integers m and n. If f(1), f(2) and f(3) are positive integers, f(1) < f(2), and f(24) = 54, then what is the value of f(18)?
A. 8
B. 9
C. 10
D. 11
E. 12
Given: f(24) = 54
Since f(mn) = f(m)f(n), we can write: [f(2)][f(2)][f(2)][f(3)] = 54
Find prime factorization of 54 to get:
[f(2)][f(2)][f(2)][f(3)] =
(3)(3)(3)(2)From this we can conclude that:
f(2) = 3 and
f(3) = 2So.... f(18) =
[f(2)][f(3)][f(3)]=
(3)(2)(2)= 12
Answer: E
Cheers,
Brent
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Brent Hanneson - founder of Greenlight Test Prep