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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]

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18 Jan 2013, 04:49
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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 _________________ Click +1 Kudos if my post helped... Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/ GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html Last edited by Bunuel on 18 Jan 2013, 04:52, edited 1 time in total. Edited the question. Math Expert Joined: 02 Sep 2009 Posts: 39695 Re: A supermarket sells a cerain brand of jelly in two jars of d [#permalink] Show Tags 18 Jan 2013, 05:05 1 This post received KUDOS Expert's post 3 This post was BOOKMARKED 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]

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24 Mar 2013, 10:24
Bunuel wrote:

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. GMAT Club Legend Joined: 09 Sep 2013 Posts: 15978 Re: A supermarket sells a cerain brand of jelly in two jars of d [#permalink] Show Tags 25 Dec 2014, 03:28 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. _________________ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 9271 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Re: A supermarket sells a cerain brand of jelly in two jars of d [#permalink] Show Tags 25 Dec 2014, 11:23 1 This post received KUDOS Expert's post 1 This post was BOOKMARKED 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. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests

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Re: A supermarket sells a cerain brand of jelly in two jars of d [#permalink]

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21 Sep 2016, 11:19
I built up on Bunuel's answers
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Re: A supermarket sells a cerain brand of jelly in two jars of d   [#permalink] 21 Sep 2016, 11:19
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