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A supermarket sells a cerain brand of jelly in two jars of d

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A supermarket sells a cerain brand of jelly in two jars of d [#permalink] New post 18 Jan 2013, 04:49
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83% (02:18) correct 16% (01:04) wrong based on 5 sessions
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A supermarket sells a certain brand of jelly in two jars of different sizes, as shown above. Jar A is a right circular cylinder with inside diameter D and inside Height h; Jar B is a right circular cylinder with inside diameter T and inside height 2h. Assuming each jar is filled to capacity, which jar of jelly will cost less per unit volume?

(1) The relationship between the diameters of Jar A and Jar B is 3T = 2D.
(2) Jar A costs $1.59 and Jar B costs 1.39


I'm interested in a detailed solution if this question was asked as a problem solving question. Any help will be appreciated. Thanks!
[Reveal] Spoiler: OA

Last edited by Bunuel on 18 Jan 2013, 04:52, edited 1 time in total.
Edited the question.
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Re: A supermarket sells a cerain brand of jelly in two jars of d [#permalink] New post 18 Jan 2013, 05:05
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A supermarket sells a certain brand of jelly in two jars of different sizes, as shown above. Jar A is a right circular cylinder with inside diameter D and inside Height h; Jar B is a right circular cylinder with inside diameter T and inside height 2h. Assuming each jar is filled to capacity, which jar of jelly will cost less per unit volume?

(1) The relationship between the diameters of Jar A and Jar B is 3T = 2D.
(2) Jar A costs $1.59 and Jar B costs 1.39

The volume of a cylinder is given by: volume_{cylinder}=\pi*{r^2}*h.

From (1) we have that t/2=d/3, thus volume_A=\pi*{(\frac{d}{2})^2}*h and volume_B=\pi*{(\frac{t}{2})^2}*2h=\pi*{(\frac{d}{3})^2}*2h.

From (2) we have that 1 unit volume of A costs \frac{1.59}{\pi*{(\frac{d}{2})^2}*h}=\frac{4*1.59}{\pi{d^2}h} and 1 unit volume of B costs \frac{1.39}{\pi*{(\frac{d}{3})^2}*2h}=\frac{4.5*1.39}{\pi{d^2}h}. Now, all we need to do is to see which one is less 4*1.59 or 4.5*1.39.

Hope it's clear.
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Re: A supermarket sells a cerain brand of jelly in two jars of d [#permalink] New post 24 Mar 2013, 10:24
Bunuel wrote:
Image
A supermarket sells a certain brand of jelly in two jars of different sizes, as shown above. Jar A is a right circular cylinder with inside diameter D and inside Height h; Jar B is a right circular cylinder with inside diameter T and inside height 2h. Assuming each jar is filled to capacity, which jar of jelly will cost less per unit volume?

(1) The relationship between the diameters of Jar A and Jar B is 3T = 2D.
(2) Jar A costs $1.59 and Jar B costs 1.39

The volume of a cylinder is given by: volume_{cylinder}=\pi*{r^2}*h.

From (1) we have that t/2=d/3, thus volume_A=\pi*{(\frac{d}{2})^2}*h and volume_B=\pi*{(\frac{t}{2})^2}*2h=\pi*{(\frac{d}{3})^2}*2h.

From (2) we have that 1 unit volume of A costs \frac{1.59}{\pi*{(\frac{d}{2})^2}*h}=\frac{4*1.59}{\pi{d^2}h} and 1 unit volume of B costs \frac{1.39}{\pi*{(\frac{d}{3})^2}*2h}=\frac{4.5*1.39}{\pi{d^2}h}. Now, all we need to do is to see which one is less 4*1.59 or 4.5*1.39.

Hope it's clear.


Bunuel - Actually my confusion arises with the answer explanation on prep, it says 1.39 / (pi*(2/9D)^2*h) = 6.255 / (pi*D^2*h). I know this is simple algebra but can you walk me through how I could easily convert this in 2 min if I were not able to see that t/2=d/3 and I kept it in the form T=2/3D. Thanks so much for your help with these problems.
Re: A supermarket sells a cerain brand of jelly in two jars of d   [#permalink] 24 Mar 2013, 10:24
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