The portion in red reflects the intent of the problem.
gmattesttaker2 wrote:
Function f(s) equals the sum of the exponents in the prime break-up of s.
For example: f(120) = 5, since 120 = (2³)(3¹)(5¹), and 3 + 1 + 1 = 5. If
f(m) = 4 and f(n) = 5, what is the value of f(mn)?
(A) 4
(B) 5
(C) 9
(D) 18
(E) 20
OA: C
f(x) = the sum of the exponents when x is prime-factored.
To illustrate:
If x = 2³3�, then f(2³3�) = 3+4 = 7.
If x = 5²11�, then f(5²11�) = 2+8 = 10.
But there is no requirement that the prime-factorization of x be composed of more than one exponent.
If the prime-factorization of x is composed of only ONE exponent, then that ONE exponent is also the SUM of the exponents:
If x = 2³, then f(2³) = 3.
Since f(m) = 4, let m = 2�.
Since f(n) = 5, let n = 2�.
Result:
f(mn) = f(2�2�) = f(2�) = 9.
The correct answer is
C.
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