It is currently 23 Nov 2017, 13:43

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 28 May 2009
Posts: 155

Kudos [?]: 267 [1], given: 91

Location: United States
Concentration: Strategy, General Management
GMAT Date: 03-22-2013
GPA: 3.57
WE: Information Technology (Consulting)
If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink]

### Show Tags

04 Feb 2013, 13:34
1
KUDOS
7
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

64% (01:04) correct 36% (01:06) wrong based on 286 sessions

### HideShow 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
[Reveal] Spoiler: OA

_________________

Kudos [?]: 267 [1], given: 91

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7747

Kudos [?]: 17869 [5], given: 235

Location: Pune, India
Re: If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink]

### Show Tags

04 Feb 2013, 21:19
5
KUDOS
Expert's post
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.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 17869 [5], given: 235

Manager
Joined: 18 Oct 2011
Posts: 89

Kudos [?]: 91 [1], given: 0

Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
Re: If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink]

### Show Tags

04 Feb 2013, 14:05
1
KUDOS
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.

Kudos [?]: 91 [1], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 42338

Kudos [?]: 133142 [1], given: 12415

Re: If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink]

### Show Tags

05 Feb 2013, 03:01
1
KUDOS
Expert's post
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
_________________

Kudos [?]: 133142 [1], given: 12415

Manager
Joined: 27 Feb 2012
Posts: 136

Kudos [?]: 64 [0], given: 22

Re: If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink]

### Show Tags

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
_________________

---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Please +1 KUDO if my post helps. Thank you.

Kudos [?]: 64 [0], given: 22

Non-Human User
Joined: 09 Sep 2013
Posts: 15508

Kudos [?]: 283 [0], given: 0

Re: If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink]

### Show Tags

19 May 2014, 21:41
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.
_________________

Kudos [?]: 283 [0], given: 0

Non-Human User
Joined: 09 Sep 2013
Posts: 15508

Kudos [?]: 283 [0], given: 0

Re: If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink]

### Show Tags

05 Aug 2015, 23:50
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.
_________________

Kudos [?]: 283 [0], given: 0

Non-Human User
Joined: 09 Sep 2013
Posts: 15508

Kudos [?]: 283 [0], given: 0

Re: If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink]

### Show Tags

18 Sep 2016, 23:48
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.
_________________

Kudos [?]: 283 [0], given: 0

Intern
Joined: 20 Sep 2016
Posts: 1

Kudos [?]: [0], given: 0

Re: If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink]

### Show Tags

28 Sep 2016, 07:43
Either m or n is 3,
so "E" is correct

Kudos [?]: [0], given: 0

Intern
Joined: 23 Jun 2016
Posts: 42

Kudos [?]: 5 [0], given: 13

Re: If k is a multiple of 3 and k = (m^2)n, where m and n are [#permalink]

### Show Tags

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

Kudos [?]: 5 [0], given: 13

Re: If k is a multiple of 3 and k = (m^2)n, where m and n are   [#permalink] 28 Sep 2016, 12:42
Display posts from previous: Sort by