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# The cost of a square slab is proportional to its thickness a

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Manager
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The cost of a square slab is proportional to its thickness a [#permalink]  19 Jul 2008, 20:29
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The cost of a square slab is proportional to its thickness and also proportional to the square of its length. What is the cost of a square slab that is 3 meters long and 0.1m thick.

(1) The cost of a square slab that is 2m long and 0.2 m thick is $160 more than the cost of a slab that is 2m long and 0.1 m thick (2) The cost of a square slab that is 3 m long and 0.1 m thick is 200 more than the cost of a square slab that is 2m long and 0.1 m thick [Reveal] Spoiler: OA Director Joined: 10 Sep 2007 Posts: 951 Followers: 7 Kudos [?]: 172 [1] , given: 0 Re: DS - square slab [#permalink] 19 Jul 2008, 20:47 1 This post received KUDOS As per questions c = ktl^2 where c is the cost, t is the thickness, l is the length and k is coefficient of proportionality. 1) k*0.2*4 - k*0.1*4 = 160. This will give us k = 400 Answer to question c = 400*0.1*9 = 360 2) k*0.1*9 - k*0.1*4 = 200. This will give us k = 400 Answer to question c = 400*0.1*9 = 360 Both option answers the question, so D. Manager Joined: 18 Jun 2007 Posts: 69 Followers: 1 Kudos [?]: 1 [0], given: 0 Re: DS - square slab [#permalink] 19 Jul 2008, 20:55 I read this question wrong. I was thinking that the cost was different for the length vs the thickness..... thx.. Senior Manager Joined: 23 May 2006 Posts: 329 Followers: 2 Kudos [?]: 44 [1] , given: 0 Re: DS - square slab [#permalink] 19 Jul 2008, 20:56 1 This post received KUDOS The cost of a square slab is proportional to its thickness and also proportional to the square of its length. What is the cost of a square slab that is 3 meters long and 0.1m thick. (1) The cost of a square slab that is 2m long and 0.2 m thick is$160 more than the cost of a slab that is 2m long and 0.1 m thick
area1 = 2x2x0.2 = 0.4m^2; area2 = 2x2x0.1 = 0.2m^2
A1 - A2 = 0.2m^2 = $160; so you can calculate the area of 0.1m^2 and you know that the are of the salb in question is 3x3x.1 = 0.9m^2 (2) The cost of a square slab that is 3 m long and 0.1 m thick is 200 more than the cost of a square slab that is 2m long and 0.1 m thick Follow same logic as S1. Ans: D SVP Joined: 16 Jul 2009 Posts: 1634 Schools: CBS WE 1: 4 years (Consulting) Followers: 28 Kudos [?]: 171 [0], given: 2 Proportionality (Disagree with OA) [#permalink] 07 Sep 2009, 11:46 Attached. Attachments DS.jpg [ 91.34 KiB | Viewed 1483 times ] _________________ The sky is the limit 800 is the limit SVP Joined: 16 Jul 2009 Posts: 1634 Schools: CBS WE 1: 4 years (Consulting) Followers: 28 Kudos [?]: 171 [0], given: 2 Re: Proportionality (Disagree with OA) [#permalink] 07 Sep 2009, 11:50 One clue for my view: the cost can be proportional to both thickness and length but with different proportionality constants. I mean, to me: Cost=a*thickness+b*length^2 not Cost=a*(thickness+length^2) Thank u. _________________ The sky is the limit 800 is the limit Manager Joined: 10 Aug 2009 Posts: 130 Followers: 3 Kudos [?]: 52 [1] , given: 10 Re: Proportionality (Disagree with OA) [#permalink] 07 Sep 2009, 12:46 1 This post received KUDOS I think the cost function is the following: C=k\times t\times l^2 t-thickness l-length then each statement alone is sufficient stmt1 4\times 0.2\times k=4\times 0.1\times k +160 you can solve for k sufficient stmt2 is basically similar to stmt 1... 9\times 0.1\times k=4\times 0.1\times k +200 you cansolve for k sufficient SVP Joined: 16 Jul 2009 Posts: 1634 Schools: CBS WE 1: 4 years (Consulting) Followers: 28 Kudos [?]: 171 [0], given: 2 Re: Proportionality (Disagree with OA) [#permalink] 07 Sep 2009, 13:08 LenaA wrote: I think the cost function is the following: C=k\times t\times l^2 t-thickness l-length then each statement alone is sufficient stmt1 4\times 0.2\times k=4\times 0.1\times k +160 you can solve for k sufficient stmt2 is basically similar to stmt 1... 9\times 0.1\times k=4\times 0.1\times k +200 you cansolve for k sufficient In fact, that is the formula in order to be D the correct answer (as it is). But my point is, that in a very strict point of view, the proportionality constant (what you mean k), can be different for t and l, that is: Cost=k1*t+k2*l^2. So you need both statements to solve for k1 and k2, and correct answer is C. To sum up, correct answer is C. OA is D. _________________ The sky is the limit 800 is the limit Manager Joined: 10 Aug 2009 Posts: 130 Followers: 3 Kudos [?]: 52 [0], given: 10 Re: Proportionality (Disagree with OA) [#permalink] 07 Sep 2009, 14:06 you are wrong. i would suggest to research about the jointly proportional functions. if z is proptional to x (when y is constant) and z is propotional to y (when x is constant), then z is propotional to the product xy and is of the form z=Kxy SVP Joined: 16 Jul 2009 Posts: 1634 Schools: CBS WE 1: 4 years (Consulting) Followers: 28 Kudos [?]: 171 [0], given: 2 Re: Proportionality (Disagree with OA) [#permalink] 07 Sep 2009, 14:20 LenaA wrote: you are wrong. i would suggest to research about the jointly proportional functions. if z is proptional to x (when y is constant) and z is propotional to y (when x is constant), then z is propotional to the product xy and is of the form z=Kxy Correct. Thank u. Dont know in what i was thinking about! D is the one _________________ The sky is the limit 800 is the limit Intern Joined: 03 Sep 2009 Posts: 30 Followers: 0 Kudos [?]: 7 [0], given: 1 Re: Proportionality (Disagree with OA) [#permalink] 07 Sep 2009, 14:32 We have only one value missing (here it's K) so it's sure that each statement is sufficient. noboru wrote: LenaA wrote: you are wrong. i would suggest to research about the jointly proportional functions. if z is proptional to x (when y is constant) and z is propotional to y (when x is constant), then z is propotional to the product xy and is of the form z=Kxy Correct. Thank u. Dont know in what i was thinking about! D is the one Manager Joined: 27 Feb 2012 Posts: 139 Followers: 1 Kudos [?]: 12 [2] , given: 22 Re: The cost of a square slab is proportional to its thickness a [#permalink] 19 Jan 2013, 02:01 2 This post received KUDOS kiyo0610 wrote: The cost of a square slab is proportional to its thickness and also proportional to the square of its length. What is the cost of a square slab that is 3 meters long and 0.1 meter thick? (1)The cost of a square slab that is 2 meters long and 0.2 meter thick is$160 more than the cost of a square slab that is 2 meters long and 0.1 meter thick.
(2)The cost of a square slab that is 3 meters long and 0.1 meter thick is \$200 more than the cost of a square slab that is 2 meters long and 0.1 meter thick.

Cost C
1) C proportional to Thickness t
2) C proportional to Length square l^2

C = K t l^2

We need to know constant K to find the answer.

Option 1: C1 and C2 difference is given for some thickness and length. We can find the constant
Option 2: Same as option1
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Re: The cost of a square slab is proportional to its thickness [#permalink]  09 Sep 2013, 06:04
I formed equation for cost as :

C prop to l^2
C prop to t

C = kl^2 + rt
l= for length
t= for thickness.
k and r constant of respective proportionality.

But in above mentioned solution it is taken as product.

I am not 100% satisfied with the derived proportionality as the product of length and thickness.

May be I am not able to identify the keyword in the question which governs product of two variables.
Or lacking some basic concept, kindly help me to interpret the language of question into a equation.
Please also share any theoretical stuff, which I should refer to understand concept of proportionality.

Thanks
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Re: The cost of a square slab is proportional to its thickness [#permalink]  10 Sep 2013, 00:38
Expert's post
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Merging similar topics.
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Re: The cost of a square slab is proportional to its thickness [#permalink]  11 Sep 2013, 04:12
When I first attempted to solve this problem I was a little thrown off by the question just saying proportional, and not directly proportional or indirectly proportional. I now realize that solving this problem is independent of the direct vs. indirect, you may get different values for the cost, but regardless you'll be able to get a value => sufficient.

My question is, can you assume that it's directly proportional from the question stem? Looking at a few of the answers above, it seems that some people have. If this was a P.S. problem instead of a D.S., the answer would depend on this assumption.

Thanks in advance for any help.
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Re: The cost of a square slab is proportional to its thickness [#permalink]  27 Oct 2013, 02:32
Cost is equal to

C = X t l^2, where X is a constant, L is length and t is thickness

FS 1=> X ( 0.2) (2^2) - X (0.1) (2^2) = 160 => X=400

We can solve for X its sufficient

FS 2=> X (0.1) (3^2) - X (0.1) (2^2) = 200=> X=400
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Re: Proportionality (Disagree with OA) [#permalink]  25 Nov 2013, 02:01
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