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

 It is currently 19 Oct 2019, 05:17 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If the price of a commodity is directly proportional to m^3

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Manager  Status: Breaking my head!!
Joined: 27 Jan 2013
Posts: 64
Location: India
Concentration: General Management, Operations
GMAT 1: 740 Q50 V40 GPA: 3.51
WE: Other (Transportation)
If the price of a commodity is directly proportional to m^3  [#permalink]

Show Tags

3
20 00:00

Difficulty:   75% (hard)

Question Stats: 54% (02:09) correct 46% (01:58) wrong based on 750 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

Originally posted by Dipankar6435 on 07 Apr 2013, 05:45.
Last edited by Bunuel on 07 Apr 2013, 22:20, edited 1 time in total.
RENAMED THE TOPIC.
Manager  Joined: 09 Feb 2013
Posts: 111
Re: Price of a commodity  [#permalink]

Show Tags

8
3
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.

Originally posted by emmak on 07 Apr 2013, 05:56.
Last edited by emmak on 07 Apr 2013, 06:00, edited 1 time in total.
General Discussion
VP  Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1019
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: Price of a commodity  [#permalink]

Show Tags

3
Dipankar6435 wrote:
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.
Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]
Math Expert V
Joined: 02 Sep 2009
Posts: 58449
If the price of a commodity is directly proportional to m^3  [#permalink]

Show Tags

2
Dipankar6435 wrote:
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

Similar questions to practice:

DS:
the-amount-of-coal-a-train-burns-each-mile-is-directly-93667.html

PS:
a-is-directly-proportional-to-b-when-a-8-b-88971.html
in-a-certain-formula-p-is-directly-proportional-to-s-and-80941.html
the-rate-of-a-chemical-reaction-is-directly-proportional-to-76921.html

Hope it helps.
_________________
Intern  Joined: 22 Jan 2010
Posts: 24
Location: India
Concentration: Finance, Technology
GPA: 3.5
WE: Programming (Telecommunications)
Re: If the price of a commodity is directly proportional to m^3  [#permalink]

Show Tags

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

Ans : Option D.
Intern  Joined: 06 Feb 2013
Posts: 48
Re: If the price of a commodity is directly proportional to m^3  [#permalink]

Show Tags

2
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
VP  Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1019
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: If the price of a commodity is directly proportional to m^3  [#permalink]

Show Tags

4
1
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 doesnt 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.
Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]
Intern  Joined: 06 Feb 2013
Posts: 48
Re: If the price of a commodity is directly proportional to m^3  [#permalink]

Show Tags

3
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 doesnt 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
VP  Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1019
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: If the price of a commodity is directly proportional to m^3  [#permalink]

Show Tags

4
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= $$m^3$$] and inversely 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.
Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]
Intern  Joined: 06 Feb 2013
Posts: 48
Re: If the price of a commodity is directly proportional to m^3  [#permalink]

Show Tags

Got it! Thanks much for help.
_________________
There are times when I do not mind kudos...I do enjoy giving some for help
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India
Re: If the price of a commodity is directly proportional to m^3  [#permalink]

Show Tags

1
3
Dipankar6435 wrote:
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:

http://www.veritasprep.com/blog/2013/01 ... -directly/
http://www.veritasprep.com/blog/2013/02 ... inversely/
http://www.veritasprep.com/blog/2013/02 ... g-jointly/
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Intern  Joined: 30 Jun 2017
Posts: 1
Re: If the price of a commodity is directly proportional to m^3  [#permalink]

Show Tags

not sure why i dont understand this, but why does

30^3 / 36^2 = (30)(30)(30) / (36)(36) = (5)(5)(5) / 6

?
Math Expert V
Joined: 02 Sep 2009
Posts: 58449
If the price of a commodity is directly proportional to m^3  [#permalink]

Show Tags

krebsbr wrote:
not sure why i dont understand this, but why does

30^3 / 36^2 = (30)(30)(30) / (36)(36) = (5)(5)(5) / 6

?

$$\frac{30^3}{36^2} = \frac{30*30*30}{36*36} =\frac{(5*6)*(5*6)*(5*6)}{(6*6)*(6*6)}=\frac{5*5*5}{6}$$

Hope it helps.
_________________
Non-Human User Joined: 09 Sep 2013
Posts: 13271
Re: If the price of a commodity is directly proportional to m^3  [#permalink]

Show Tags

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] 20 Dec 2018, 20:59
Display posts from previous: Sort by

If the price of a commodity is directly proportional to m^3

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  