NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 13:24 It is currently 25 Apr 2024, 13:24
Decision Tracker
My Rewards
New posts
New comers' posts

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

If k is a multiple of 3 and k = (m^2)n, where m and n are

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
megafan
Manager
Manager
Joined: 28 May 2009
Posts: 139
Own Kudos [?]: 797 [26]
Given Kudos: 91
Location: United States
Concentration: Strategy, General Management
Schools: Booth PT '18 Stern PT Fall'18
GMAT Date: 03-22-2013
GPA: 3.57
WE:Information Technology (Consulting)
Send PM
GMAT ToolKit User
If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink] New post   04 Feb 2013, 13:34
6
Kudos
19
Bookmarks
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

65% (01:35) correct 35% (01:43) wrong based on 469 sessions
Hide Show timer Statistics
If k is a multiple of 3 and \(k = (m^2)n\), where m and n are prime numbers, which of the following must be a multiple of 9?

(A) \(m^2\)
(B) \(n^2\)
(C) \(mn\)
(D) \(mn^2\)
(E) \((mn)^2\)

Source: Gmat Hacks 1800
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14823
Own Kudos [?]: 64921 [13]
Given Kudos: 426
Location: Pune, India
Send PM
Re: If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink] New post   04 Feb 2013, 21:19
10
Kudos
3
Bookmarks
Expert Reply
megafan wrote:
If k is a multiple of 3 and \(k = (m^2)n\), where m and n are prime numbers, which of the following must be a multiple of 9?

(A) \(m^2\)
(B) \(n^2\)
(C) \(mn\)
(D) \(mn^2\)
(E) \((mn)^2\)

Source: Gmat Hacks 1800


Given prime factorization of k:
\(k = (m^2)n\),
If k is a multiple of 3, we can say that either m = 3 or n = 3.
So either m^2 or n^2 will be a multiple of 9 but we don't know which of them is a multiple of 9.
That is why none of A, B, C and D work.
(E) \((mn)^2\) includes both\(m^2\) and \(n^2\) and hence it must be a multiple of 9.
General Discussion
User avatar
sambam
Manager
Manager
Joined: 18 Oct 2011
Posts: 58
Own Kudos [?]: 353 [2]
Given Kudos: 0
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
Send PM
Re: If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink] New post   04 Feb 2013, 14:05
1
Kudos
1
Bookmarks
Since 'm' and 'n' are primes, In order for k to be a multiple of 3 either 'n' or 'm' must be 3. Also, In order to be a multiple of 9 the product must have two 3's as factors.
A) No. 'm' could be 3 or 'n' could be 3 we don't know which one
B) No. Same logic as above.
C) No. 'm' and 'n' could both be 3 in which case it would work. But they could also be '5' and '7' or some other pair of primes.
D) No. n^2 could be 3^2 or it could be 5^2 (or some other prime number)
E) Correct Answer. Since 3 must be one of the numbers, squaring the product must yield 9 as a factor.
User avatar
BangOn
Manager
Manager
Joined: 27 Feb 2012
Posts: 97
Own Kudos [?]: 170 [0]
Given Kudos: 22
Send PM
Re: If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink] New post   04 Feb 2013, 14:28
megafan wrote:
If k is a multiple of 3 and \(k = (m^2)n\), where m and n are prime numbers, which of the following must be a multiple of 9?

(A) \(m^2\)
(B) \(n^2\)
(C) \(mn\)
(D) \(mn^2\)
(E) \((mn)^2\)

Source: Gmat Hacks 1800



must be a multiple of 9
m and n are prime...lets have 2 and 3
now either of then can be a 3...
a) m can be 2 and n = 3...out
b) n can be 2 and m = 3...out
c) m = 2 and n=3 ...out
d) n can be 2 and m = 3...out
e) m = 2/3 or n = 3/2 both satisfies .......must be a multiple of 9
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619010 [1]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink] New post   05 Feb 2013, 03:01
1
Kudos
Expert Reply
megafan wrote:
If k is a multiple of 3 and \(k = (m^2)n\), where m and n are prime numbers, which of the following must be a multiple of 9?

(A) \(m^2\)
(B) \(n^2\)
(C) \(mn\)
(D) \(mn^2\)
(E) \((mn)^2\)

Source: Gmat Hacks 1800


This question is almost exact copy of the following GMAT Prep question: if-is-n-is-multiple-of-5-and-n-p-2-q-where-p-and-q-are-prim-92383.html
avatar
sahniminie
Intern
Intern
Joined: 20 Sep 2016
Posts: 1
Own Kudos [?]: [0]
Given Kudos: 0
Send PM
Re: If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink] New post   28 Sep 2016, 07:43
Either m or n is 3,
so "E" is correct
avatar
Akuthiala
Intern
Intern
Joined: 23 Jun 2016
Posts: 34
Own Kudos [?]: 10 [0]
Given Kudos: 13
Send PM
Re: If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink] New post   28 Sep 2016, 12:42
A) No since n could be 9
B) No since m=3
C) No since m could be 2 and n=3
D) No since M could 3 and n=2
E) Yes since either M or N have to be 3 (or factor) so they will become a factor of 9
User avatar
D
BrushMyQuant
Tutor
Joined: 05 Apr 2011
Status:Tutor - BrushMyQuant
Posts: 1777
Own Kudos [?]: 2094 [0]
Given Kudos: 100
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Send PM
If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink] New post   04 Sep 2021, 08:56
Expert Reply
Top Contributor
If k is a multiple of 3 and \(k = (m^2)n\) then \((m^2)n\) will also be a multiple of 3

Since both m and n are prime numbers, so either m is 3 or n is 3 or both are 3
In any case, m*n will be a multiple of 3
=> \((mn)^2\) will be a multiple of \(3^2\) or 9

So, \(Answer will be E\)
Hope it helps!
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32679
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink] New post   03 Apr 2023, 12:07
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink]
03 Apr 2023, 12:07
Moderators:
Bunuel
Math Expert
92914 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions