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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

If 5400mn = k4, where m, n, and k are positive integers, what is the least possible value of m + n? (A) 11 (B) 18 (C) 20 (D) 25 (E) 33

banksy please format the questions properly!

Question should read: If 5400mn = k^4, where m, n, and k are positive integers, what is the least possible value of m + n? A. 11 B. 18 C. 20 D. 25 E. 33

Note that m, n, and k are positive integers.

First of all: \(5,400=2^3*3^3*5^2\). Now, in order \(5,400mn=2^3*3^3*5^2*m*n\) to be equal to the integer in fourth power then \(mn\) must complete the powers of 2, 3 and 5 to the fourth power, hence the least value of \(mn\) for which \(2^3*3^3*5^2*m*n=k^4\) is for \(mn=2*3*5^2=150\). In this case \(5,400mn=2^3*3^3*5^2*(2*3*5^2)=(2*3*5)^4=k^4\).

So we have that the least value of \(mn\) is \(2*3*5^2\). Next: in order to minimize \(m+n\) we should break \(2*3*5^2\) into two multiples which are closest to each other: \(2*5=10\) and \(3*5=15\), their sum is \(10+15=25\).

Re: If 5400mn = k4, where m, n, and k are positive integers [#permalink]

Show Tags

27 Feb 2011, 02:38

Bunuel wrote:

banksy wrote:

If 5400mn = k4, where m, n, and k are positive integers, what is the least possible value of m + n? (A) 11 (B) 18 (C) 20 (D) 25 (E) 33

banksy please format the questions properly!

Question should read: If 5400mn = k^4, where m, n, and k are positive integers, what is the least possible value of m + n? A. 11 B. 18 C. 20 D. 25 E. 33

Note that m, n, and k are positive integers.

First of all: \(5,400=2^3*3^3*5^2\). Now, in order \(5,400mn=2^3*3^3*5^2*m*n\) to be equal to the integer in fourth power then \(mn\) must complete the powers of 2, 3 and 5 to the fourth power, hence the least value of \(mn\) for which \(2^3*3^3*5^2*m*n=k^4\) is for \(mn=2*3*5^2=150\). In this case \(5,400mn=2^3*3^3*5^2*(2*3*5^2)=(2*3*5)^4=k^4\).

So we have that the least value of \(mn\) is \(2*3*5^2\). Next: in order to minimize \(m+n\) we should break \(2*3*5^2\) into two multiples which are closest to each other: \(2*5=10\) and \(3*5=15\), their sum is \(10+15=25\).

Answer: D.

I did not understand the following parts. m*n=2*3*5^2=150, and So we have that the least value of \(mn\) is \(2*3*5^2\). Next: in order to minimize \(m+n\) we should break \(2*3*5^2\) into two multiples which are closest to each other: \(2*5=10\) and \(3*5=15\), their sum is \(10+15=25\).
_________________

If 5400mn = k4, where m, n, and k are positive integers, what is the least possible value of m + n? (A) 11 (B) 18 (C) 20 (D) 25 (E) 33

banksy please format the questions properly!

Question should read: If 5400mn = k^4, where m, n, and k are positive integers, what is the least possible value of m + n? A. 11 B. 18 C. 20 D. 25 E. 33

Note that m, n, and k are positive integers.

First of all: \(5,400=2^3*3^3*5^2\). Now, in order \(5,400mn=2^3*3^3*5^2*m*n\) to be equal to the integer in fourth power then \(mn\) must complete the powers of 2, 3 and 5 to the fourth power, hence the least value of \(mn\) for which \(2^3*3^3*5^2*m*n=k^4\) is for \(mn=2*3*5^2=150\). In this case \(5,400mn=2^3*3^3*5^2*(2*3*5^2)=(2*3*5)^4=k^4\).

So we have that the least value of \(mn\) is \(2*3*5^2\). Next: in order to minimize \(m+n\) we should break \(2*3*5^2\) into two multiples which are closest to each other: \(2*5=10\) and \(3*5=15\), their sum is \(10+15=25\).

Answer: D.

I did not understand the following parts. m*n=2*3*5^2=150, and So we have that the least value of \(mn\) is \(2*3*5^2\). Next: in order to minimize \(m+n\) we should break \(2*3*5^2\) into two multiples which are closest to each other: \(2*5=10\) and \(3*5=15\), their sum is \(10+15=25\).

As explained before in order \(5,400mn=2^3*3^3*5^2*m*n\) to be equal to the integer in fourth power then \(mn\) must complete the powers of 2, 3 and 5 to the fourth power er (well generally to the multiple of 4, though as we need the least value of mn then to 4), hence the least value of \(mn\) for which \(2^3*3^3*5^2*m*n=k^4\) is for \(mn=2*3*5^2=150\). In this case \(5,400mn=2^3*3^3*5^2*(2*3*5^2)=(2*3*5)^4=k^4\): mn must have one 2 to complete 2^3 to 2^4, one 3 to complete 3^3 to 3^4 and two 5's to complete 5^2 to 5^4.

So we have that the least value of \(mn\) is \(2*3*5^2\). Next: in order to minimize \(m+n\) (taking into account that \(mn=2*3*5^2\)) we should break \(2*3*5^2\) into two multiples which are closest to each other: \(2*5=10\) and \(3*5=15\), their sum is \(10+15=25\) (all other break downs of \(mn=2*3*5^2=150\) will have the greater sum: 1+150=151, 2+75=77, 3+50=52, ...).

Re: If 5400mn = k^4, where m, n, and k are positive integers [#permalink]

Show Tags

18 Jun 2014, 14:31

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 5400mn = k^4, where m, n, and k are positive integers [#permalink]

Show Tags

17 Sep 2015, 00:01

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 5400mn = k^4, where m, n, and k are positive integers [#permalink]

Show Tags

24 Oct 2016, 05:56

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 5400mn = k^4, where m, n, and k are positive integers [#permalink]

Show Tags

28 Dec 2016, 09:33

Excellent Question from KAPLAN. Here is my response to this one => As k is a postive integer => K^4 will be a perfect fourth power 5400=2^3*5^2*3^3 Least value of m*n=> 2*3*5^2

Hence Least value of m+n => 10+15 = 25

Hence D _________________

Give me a hell yeah ...!!!!!

gmatclubot

Re: If 5400mn = k^4, where m, n, and k are positive integers
[#permalink]
28 Dec 2016, 09:33

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...