GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 25 Sep 2018, 20:33

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

If m and n are positive integer, and 1800m = n3, what is

Author Message
TAGS:

Hide Tags

Intern
Joined: 09 Feb 2011
Posts: 15
If m and n are positive integer, and 1800m = n3, what is  [#permalink]

Show Tags

Updated on: 21 Aug 2013, 09:38
5
7
00:00

Difficulty:

5% (low)

Question Stats:

81% (01:16) correct 19% (01:37) wrong based on 553 sessions

HideShow timer Statistics

If m and n are positive integer, and $$1800m = n^3$$, what is the least possible value of m?
(A) 2
(B) 3
(C) 15
(D) 30
(E) 45

Originally posted by loveparis on 09 Feb 2011, 17:32.
Last edited by Narenn on 21 Aug 2013, 09:38, edited 1 time in total.
Minor Edit
Math Expert
Joined: 02 Sep 2009
Posts: 49496
Re: If m and n are positive integer, and 1800m = n3, what is  [#permalink]

Show Tags

09 Feb 2011, 17:57
4
3
loveparis wrote:
89. If m and n are positive integer, and 1800m = n3, what is the least possible value of m?
(A) 2
(B) 3
(C) 15
(D) 30
(E) 45

$$1800m=2^3*3^2*5^2*m=n^3$$ the least value of $$m$$ for which $$2^3*3^2*5^2*m$$ is a perfect cube is 3*5=15 (m must complete the powers of 3 and 5 to cubes): in this case $$2^3*3^2*5^2*m=2^3*3^3*5^3=(2*3*5)^3=n^3$$

_________________
General Discussion
Manager
Joined: 22 Aug 2008
Posts: 156
Re: If m and n are positive integer, and 1800m = n3, what is  [#permalink]

Show Tags

09 Feb 2011, 17:55
1
1
1800*m=n^3
m=n^3/1800
=n^3/(3^2*5^2*2^3)

so n has to be 3*5*2 so that n^3 is divisible by 1800.

So m= (2*3*5)^3/(3^2*5^2*2^3)
m=15
Manager
Joined: 24 Oct 2012
Posts: 63
WE: Information Technology (Computer Software)
Re: If m and n are positive integer, and 1800m = n3, what is  [#permalink]

Show Tags

18 Jun 2014, 21:04
1
Hi
This is one of the questions in which plugin the answers will make it much easier.

2.3.15.30.45

1800 *2 = 3600 not a cube
b) 3
5400 not a cube
c) 1800 * 15 = 27000 = 30 to the power of 3

d) and e) are higher, so no need to go ahead further.
ans : C
Current Student
Joined: 12 Aug 2015
Posts: 2647
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If m and n are positive integer, and 1800m = n3, what is  [#permalink]

Show Tags

16 Mar 2016, 01:39
Manager
Joined: 09 Jun 2015
Posts: 97
Re: If m and n are positive integer, and 1800m = n3, what is  [#permalink]

Show Tags

16 Mar 2016, 02:04
loveparis wrote:
If m and n are positive integer, and $$1800m = n^3$$, what is the least possible value of m?
(A) 2
(B) 3
(C) 15
(D) 30
(E) 45

1800*m is a cube number'
The first cube number is 27000 when m = 15
Tip: Prime factor 1800:2^3*3^2*5^2; we require one more 3 and one more 5.
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2835
Re: If m and n are positive integer, and 1800m = n3, what is  [#permalink]

Show Tags

02 May 2017, 16:44
2
1
loveparis wrote:
If m and n are positive integer, and $$1800m = n^3$$, what is the least possible value of m?
(A) 2
(B) 3
(C) 15
(D) 30
(E) 45

Since 1800m = n^3, we can say that the product of 1800 and some integer m is equal to a perfect cube.
We must remember that all perfect cubes break down to unique prime factors, each of which has an exponent that is a multiple of 3. So, let’s break down 1800 into primes to help determine what extra prime factors we need to make 1800m a perfect cube.

1800 = 18 x 100 = 2 x 9 x 10 x 10 = 2 x 3 x 3 x 2 x 5 x 2 x 5 = 2^3 x 3^2 x 5^2

In order to make 1800n a perfect cube, we need one more 3 and one more 5. Thus, the least value of m is 3 x 5 = 15.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Non-Human User
Joined: 09 Sep 2013
Posts: 8195
Re: If m and n are positive integer, and 1800m = n3, what is  [#permalink]

Show Tags

08 Jul 2018, 02:27
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.
_________________
Re: If m and n are positive integer, and 1800m = n3, what is &nbs [#permalink] 08 Jul 2018, 02:27
Display posts from previous: Sort by

If m and n are positive integer, and 1800m = n3, what is

Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.