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Re: Let f be a function such that f(mn) = f(m)f(n) for every positive inte [#permalink]
Bunuel 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

Are You Up For the Challenge: 700 Level Questions


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)?

f(1) = f(1)*f(1) ; f(1) = 1
f(2) > 1; Let f(2) be a; and let f(3) = b; where a & b are positive integers
f(24) = {f(2)}^3*f(3) = 54
a^3*b = 54 = 3^3*2; a = 3; b = 2
f(18) = {f(3)}^2*f(2) = b^2*a = 4*3 = 12

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Re: Let f be a function such that f(mn) = f(m)f(n) for every positive inte [#permalink]
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Re: Let f be a function such that f(mn) = f(m)f(n) for every positive inte [#permalink]
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