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Let f be a function such that f(mn) = f(m)f(n) for every pos
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23 Apr 2020, 10:27
23 Apr 2020, 10:27
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Question Stats:
52% (03:07) correct
47% (02:40) wrong based on 69 sessions
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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
A. 8
B. 9
C. 10
D. 11
E. 12
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Re: Let f be a function such that f(mn) = f(m)f(n) for every pos
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23 Apr 2020, 12:41
23 Apr 2020, 12:41
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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
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) = 2
So.... f(18) = [f(2)][f(3)][f(3)]
= (3)(2)(2)
= 12
Answer: E
Cheers,
Brent
General Discussion
Re: Let f be a function such that f(mn) = f(m)f(n) for every pos
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09 Oct 2022, 13:54
09 Oct 2022, 13:54
1
Hey, how did you think about factorize it? I am asking because I automatically thought factorization of the 24, but after 15 minutes, I still couldn't think about to factorization of the 54.
In real test time, is it just experience or is it some hint in the question?
In real test time, is it just experience or is it some hint in the question?
