Last visit was: 10 Jul 2025, 20:37 It is currently 10 Jul 2025, 20:37
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
GMAT 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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 10 Jul 2025
Posts: 102,631
Own Kudos:
740,220
 [23]
Given Kudos: 98,170
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,631
Kudos: 740,220
 [23]
Let f be a function such that f(mn) = f(m)f(n) for every positive inte 09 Apr 2020, 06:41
Kudos
Add Kudos
23
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

65% (hard)

Question Stats:

65% (02:51) correct 35% (02:52) wrong based on 181 sessions

History

Date
Time
Result
Not Attempted Yet
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
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 09 Jul 2025
Posts: 6,375
Own Kudos:
15,575
 [6]
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
My Reviews
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,375
Kudos: 15,575
 [6]
Let f be a function such that f(mn) = f(m)f(n) for every positive inte 09 Apr 2020, 06:55
2
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
Bunuel
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

Given f (mn) = f (m) f (n)
and
f(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) * f(2)
F(6) = f(3) * f(2)
F(24) = f(4) * f(6) = f(2)* f(2) * f(2) * f(3) \(= 54 = 3^3 *2\),

i.e. f(2) = 3 and f(3) =2

F(18) = f(9) * f(2) = f(3) * f(3) * f(2) = 2*2*3 = 12

Answer: Option E
General Discussion
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 13 May 2024
Posts: 6,755
Own Kudos:
34,051
 [2]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,755
Kudos: 34,051
 [2]
Let f be a function such that f(mn) = f(m)f(n) for every positive inte 09 Apr 2020, 06:57
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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

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
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 10 Jul 2025
Posts: 5,688
Own Kudos:
5,200
 [1]
Given Kudos: 161
Location: India
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
My Reviews
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
Posts: 5,688
Kudos: 5,200
 [1]
Let f be a function such that f(mn) = f(m)f(n) for every positive inte 10 Apr 2020, 06:57
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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

IMO E
User avatar
BrushMyQuant
User avatar
Joined: 05 Apr 2011
Last visit: 10 Jul 2025
Posts: 2,243
Own Kudos:
2,458
 [1]
Given Kudos: 100
Status:Tutor - BrushMyQuant
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
Posts: 2,243
Kudos: 2,458
 [1]
Let f be a function such that f(mn) = f(m)f(n) for every positive inte 22 Feb 2025, 03:50
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
↧↧↧ Detailed Video Solution to the Problem ↧↧↧



f(mn) = f(m)f(n)

f(24) = f(2*12) = f(2) * f(12) = f(2) * f(4*3) = f(2) * f(4) * f(3)
= f(2) * f(2*2) * f(3) = f(2) * f(2) * f(2) * f(3)= \(((f(2))^3 * f(3)\) = 54 = \(3^3 * 2\)
=> f(2) = 3 and f(3) = 2

f(18) = f(9*2) = f(9) * f(2) = f(3*3) * f(2) = f(3) * f(3) * f(2) = 2 * 2 * 3 = 12

So, Answer will be E
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

­
Moderators:
Bunuel
Math Expert
102631 posts
Krunaal
PS Forum Moderator
686 posts