GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Let f be a function such that f(mn) = f(m)f(n) for every pos
[#permalink]
23 Apr 2020, 10:27
23 Apr 2020, 10:27
Expert Reply
15
Bookmarks
00:00
Question Stats:
48% (02:57) correct
51% (02:40) wrong based on 64 sessions
Hide Show timer Statistics
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
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Let f be a function such that f(mn) = f(m)f(n) for every pos
[#permalink]
23 Apr 2020, 12:41
23 Apr 2020, 12:41
4
3
Bookmarks
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
[#permalink]
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?
