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 the price of a commodity is directly proportional to m^3 [#permalink]

Show Tags

07 Apr 2013, 05:45

1

This post received KUDOS

6

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

51% (02:16) correct
49% (00:51) wrong based on 309 sessions

HideShow timer Statistics

If the price of a commodity is directly proportional to m^3 and inversely proportional to q^2, which of the following values of m and q will result in the highest price for the commodity?

A. m=3, q=2 B. m=12, q=12 C. m=20, q=20 D. m=30, q=36 E. m=36, q=72

If the price of a commodity is directly proportional to m^3 and inversely proportional to q^2, which of the following values of m and q will result in the highest price for the commodity? A. m=3, q=2 B. m=12, q=12 C. m=20, q=20 D. m=30, q=36 E. m=36, q=72

Let the price is P & constant is K So P = \(\frac{K m^3}{q^2}\)

Now Just use the values in the options and put in the before mentioned equation. A) P = \(\frac{K m^3}{q^2}\) = \(\frac{K 3^3}{2^2}\) = \(\frac{K 27}{4}\) = 6.75 K B) P = \(\frac{K m^3}{q^2}\) = \(\frac{K 12^3}{12^2}\) = 12 K C) P = \(\frac{K m^3}{q^2}\) = \(\frac{K 20^3}{20^2}\) = 20 K D) P = \(\frac{K m^3}{q^2}\) = \(\frac{K 30^3}{36^2}\) = 125/6 = >20K E) P = \(\frac{K m^3}{q^2}\) = \(\frac{K 36^3}{72^2}\) = 9 K

So the answer is D. This is probably 600-700 level question.

Hope the explanation helps. _________________

Kudos will encourage many others, like me. Good Questions also deserve few KUDOS.

Last edited by emmak on 07 Apr 2013, 06:00, edited 1 time in total.

If the price of a commodity is directly proportional to m^3 and inversely proportional to q^2, which of the following values of m and q will result in the highest price for the commodity? A. m=3, q=2 B. m=12, q=12 C. m=20, q=20 D. m=30, q=36 E. m=36, q=72

Function = \(\frac{m^3}{q^2}\)

A=\(\frac{3*3*3}{2*2}=\frac{27}{4}=7\) almost B=\(\frac{12*12*12}{12*12}=12\) C=\(\frac{20*20*20}{20*20}=20\) D=\(\frac{30*30*30}{36*36}=125/6\) E=\(\frac{36*36*36}{72*72}=9\)

It's down to C or D, because \(\frac{120}{6}=20\), \(\frac{125}{6}>20\) D _________________

It is beyond a doubt that all our knowledge that begins with experience.

If the price of a commodity is directly proportional to m^3 and inversely proportional to q^2, which of the following values of m and q will result in the highest price for the commodity?

A. m=3, q=2 B. m=12, q=12 C. m=20, q=20 D. m=30, q=36 E. m=36, q=72

Re: If the price of a commodity is directly proportional to m^3 [#permalink]

Show Tags

09 Apr 2013, 04:56

Let price of the commodity be P = \(k *\)\(m^3\) /\(Q^2\)

A. P = \(k * 27/4\) = 6.75K B. P = \(K * 12^3/12^2\) = 12k C. P = \(K * 20^3/20^2\) = 20k D. P = \(K * 30^3/36^2\)= \(k*5*5*30/6*6\) = \(k * (125/6)\) = 21K (approx) E. P = \(k * 36^3/72^2\) = \(K*(36/2*2)\) = 9k

Re: If the price of a commodity is directly proportional to m^3 [#permalink]

Show Tags

10 Apr 2013, 18:09

1

This post received KUDOS

Could you please explain how you get \(\frac{m^3}{q^2}\) or \(\frac{Km^3}{q^2}\)? Where am I wrong expressing this thing firstly as \(p=m^3k\) and \(p=\frac{k}{q^2}\)? _________________

There are times when I do not mind kudos...I do enjoy giving some for help

Re: If the price of a commodity is directly proportional to m^3 [#permalink]

Show Tags

10 Apr 2013, 23:19

3

This post received KUDOS

1

This post was BOOKMARKED

obs23 wrote:

Could you please explain how you get \(\frac{m^3}{q^2}\) or \(\frac{Km^3}{q^2}\)? Where am I wrong expressing this thing firstly as \(p=m^3k\) and \(p=\frac{k}{q^2}\)?

"directly proportional to m^3 and inversely proportional to q^2" is what the text says. So if m increases the price increases, if q increases the price decreases. The right formula here is \(\frac{m^3}{q^2}\) ( or with k, it doesn`t change anything), if the numerator grows, the price does the same; and as in every fraction, if the denominator grows, the price drops. Your formulas are right but the price depends on both m and q, you have to include them in one equation.

Let me know if it is clear _________________

It is beyond a doubt that all our knowledge that begins with experience.

Re: If the price of a commodity is directly proportional to m^3 [#permalink]

Show Tags

11 Apr 2013, 03:51

1

This post received KUDOS

Zarrolou wrote:

obs23 wrote:

Could you please explain how you get \(\frac{m^3}{q^2}\) or \(\frac{Km^3}{q^2}\)? Where am I wrong expressing this thing firstly as \(p=m^3k\) and \(p=\frac{k}{q^2}\)?

"directly proportional to m^3 and inversely proportional to q^2" is what the text says. So if m increases the price increases, if q increases the price decreases. The right formula here is \(\frac{m^3}{q^2}\) ( or with k, it doesn`t change anything), if the numerator grows, the price does the same; and as in every fraction, if the denominator grows, the price drops. Your formulas are right but the price depends on both m and q, you have to include them in one equation.

Let me know if it is clear

I see that makes sense. I guess I am making it more complicated than it really is. If you say that my formulas are correct, then \(\frac{m^3}{q^2}\) should somehow be extracted from \(p=m^3k\) and \(p=\frac{k}{q^2}\), no? Technically speaking, I thought there was a way to combine them into \(\frac{m^3}{q^2}\), just from pure algebraic manipulation (which I am very interested in here)... Or is it simply about common sense or the way you explained it?

P.S. Like your "kudos" tagline man! _________________

There are times when I do not mind kudos...I do enjoy giving some for help

Re: If the price of a commodity is directly proportional to m^3 [#permalink]

Show Tags

11 Apr 2013, 04:05

3

This post received KUDOS

obs23 wrote:

I see that makes sense. I guess I am making it more complicated than it really is. If you say that my formulas are correct, then \(\frac{m^3}{q^2}\) should somehow be extracted from \(p=m^3k\) and \(p=\frac{k}{q^2}\), no? I thought there was a way to combine them into \(\frac{m^3}{q^2}\), just from pure algebraic manipulation (which I am very interested in here)... Or is it simply about common sense or the way you explained it?

P.S. Like your tagline man!

To create the formula we should refer to the text: "If the price of a commodity is directly proportional to m^3 [and at this point we write down Price= \(m^3\)] andinversely proportional to q^2 [and at this point we complete the foumula adding the Denominator so Price=\(\frac{m^3}{q^2}\)], which of the following values of m and q will result in the highest price for the commodity?" \(\frac{m^3}{q^2}\) is not extracted from \(p=m^3k\) and \(p=\frac{k}{q^2}\), and you cannot obtain it from pure algebraic manipulation. The idea behind your formulas is correct p=m^3 expresses the direct correlation between p and m; and also p=1/q^2 expresses the inverse correlation between p and q. But the text uses "and" so those ideas must be expressed in one formula, so to obtain this final formula you "complete" one with the other =>m^3/p^2 _________________

It is beyond a doubt that all our knowledge that begins with experience.

If the price of a commodity is directly proportional to m^3 and inversely proportional to q^2, which of the following values of m and q will result in the highest price for the commodity?

A. m=3, q=2 B. m=12, q=12 C. m=20, q=20 D. m=30, q=36 E. m=36, q=72

For more on direct, inverse and joint variation, check out these posts:

Re: If the price of a commodity is directly proportional to m^3 [#permalink]

Show Tags

06 Oct 2014, 13:08

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 the price of a commodity is directly proportional to m^3 [#permalink]

Show Tags

18 Nov 2015, 06:18

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. _________________

This is the kickoff for my 2016-2017 application season. After a summer of introspect and debate I have decided to relaunch my b-school application journey. Why would anyone want...

Check out this awesome article about Anderson on Poets Quants, http://poetsandquants.com/2015/01/02/uclas-anderson-school-morphs-into-a-friendly-tech-hub/ . Anderson is a great place! Sorry for the lack of updates recently. I...

Time is a weird concept. It can stretch for seemingly forever (like when you are watching the “Time to destination” clock mid-flight) and it can compress and...