Quantitative Aptitude – Algebra – Function


Slot – 1 – Quantitative Aptitude – Algebra – Function – Let f be a function such that f (mn)

Q. 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 f (18) equals?

Answer: 12

Solution: Given f (mn) = f (m) f (n)and (1), f (2) and f (3) are positive integers.
As we know F(2*1) = f(2)= f(2)*f(1), so f(1) = 1
F(4) = f(2) ^ 2
F(6) = f(3) * f(2)
F(24) = f(4) * f(6) = f(2)^3 * f(3) = 54, only f(2) = 3 and f(3) =2 satisfies the equation , so we get
F(18) = f(9) * f(2) = f(3)^2 * f(2) = 4*3 = 12

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