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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, 03:49
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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

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Last edited by Bunuel on 18 Jan 2013, 03:52, edited 1 time in total.
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Re: A supermarket sells a cerain brand of jelly in two jars of d [#permalink] New post 18 Jan 2013, 04:05
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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, 09:24
Bunuel wrote:
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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.


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.
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Re: A supermarket sells a cerain brand of jelly in two jars of d [#permalink] New post 25 Dec 2014, 02:28
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Re: A supermarket sells a cerain brand of jelly in two jars of d [#permalink] New post 25 Dec 2014, 10:23
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Hi jmuduke08,

Since this conversation is over a 1.5 years old, I'm not sure if your'e still interested in an explanation, but here goes.

On the GMAT, DS questions sometimes involve "crazy-looking" numbers as a way to test if you can "get around" the crazy numbers and get to the correct answer without doing lots of extensive calculations. In that same way, Problem Solving questions will rarely force you into doing lots of "crazy math" because the GMAT Quant section isn't really a "math test" (by traditional standards). If you CHOOSE to do lots of crazy calculations, then that's on you - most PS questions can be approached in a variety of ways though, so "your way" of doing things might be the "long way."

If the type of prompt that occurs here were to occur in a PS prompt, then you'd likely see the word "approximately" in the wording (so that you wouldn't be forced into doing long-winded and excessive calculations) and you'd have 5 answers to choose from. If the 5 answers were sufficiently "spaced out", then you wouldn't have to do much to solve the problem beyond the basic formulaic set-up, simplification and some estimation/pattern-matching.

Even here, once you combine the two Facts, the two equations have the exact same variables AND are each set equal to a value, so performing the last set of calculations is unnecessary - you KNOW you could figure out which costs less per unit volume, so that is enough to choose the correct answer.

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Re: A supermarket sells a cerain brand of jelly in two jars of d   [#permalink] 25 Dec 2014, 10:23
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