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

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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 2 meters 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 meters 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: 949 Followers: 7 Kudos [?]: 208 [2] , given: 0 Re: The cost of a square slab is proportional to its thickness a [#permalink] 19 Jul 2008, 20:47 2 This post received KUDOS 4 This post was BOOKMARKED 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 [?]: 11 [0], given: 0 Re: The cost of a square slab is proportional to its thickness a [#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: 327 Followers: 2 Kudos [?]: 115 [1] , given: 0 Re: The cost of a square slab is proportional to its thickness a [#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: 36 Kudos [?]: 415 [0], given: 2 Re: The cost of a square slab is proportional to its thickness a [#permalink] 07 Sep 2009, 11:46 Attached. Attachments DS.jpg [ 91.34 KiB | Viewed 5355 times ] _________________ The sky is the limit 800 is the limit GMAT Club Premium Membership - big benefits and savings SVP Joined: 16 Jul 2009 Posts: 1634 Schools: CBS WE 1: 4 years (Consulting) Followers: 36 Kudos [?]: 415 [0], given: 2 Re: The cost of a square slab is proportional to its thickness a [#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 GMAT Club Premium Membership - big benefits and savings Manager Joined: 10 Aug 2009 Posts: 130 Followers: 3 Kudos [?]: 58 [1] , given: 10 Re: The cost of a square slab is proportional to its thickness a [#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: 36 Kudos [?]: 415 [0], given: 2 Re: The cost of a square slab is proportional to its thickness a [#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 GMAT Club Premium Membership - big benefits and savings Manager Joined: 10 Aug 2009 Posts: 130 Followers: 3 Kudos [?]: 58 [1] , given: 10 Re: The cost of a square slab is proportional to its thickness a [#permalink] 07 Sep 2009, 14:06 1 This post received KUDOS 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: 36 Kudos [?]: 415 [0], given: 2 Re: The cost of a square slab is proportional to its thickness a [#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 GMAT Club Premium Membership - big benefits and savings Intern Joined: 03 Sep 2009 Posts: 29 Followers: 0 Kudos [?]: 8 [0], given: 1 Re: The cost of a square slab is proportional to its thickness a [#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: 138 Followers: 1 Kudos [?]: 31 [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 _________________ --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Please +1 KUDO if my post helps. Thank you. Verbal Forum Moderator Status: After a long voyage, land is visible. Joined: 22 Mar 2013 Posts: 989 Location: India GPA: 3.51 WE: Information Technology (Computer Software) Followers: 89 Kudos [?]: 648 [0], given: 222 Re: The cost of a square slab is proportional to its thickness a [#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 _________________ Piyush K ----------------------- Our greatest weakness lies in giving up. The most certain way to succeed is to try just one more time. ― Thomas A. Edison Don't forget to press--> Kudos My Articles: 1. WOULD: when to use? | 2. All GMATPrep RCs (New) Tip: Before exam a week earlier don't forget to exhaust all gmatprep problems specially for "sentence correction". Math Expert Joined: 02 Sep 2009 Posts: 27505 Followers: 4317 Kudos [?]: 42383 [0], given: 6024 Re: The cost of a square slab is proportional to its thickness a [#permalink] 10 Sep 2013, 00:38 Expert's post _____________ Merging similar topics. _________________ Intern Joined: 18 Aug 2013 Posts: 18 Followers: 0 Kudos [?]: 2 [0], given: 6 Re: The cost of a square slab is proportional to its thickness a [#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. Grant Director Joined: 29 Nov 2012 Posts: 926 Followers: 12 Kudos [?]: 456 [0], given: 543 Re: The cost of a square slab is proportional to its thickness a [#permalink] 27 Oct 2013, 02:32 1 This post was BOOKMARKED 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=> $$X (0.1) (3^2) - X (0.1) (2^2) = 200$$=> $$X=400$$ _________________ 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 gmat-prep-software-analysis-and-what-if-scenarios-146146.html GMAT Club Legend Joined: 09 Sep 2013 Posts: 4942 Followers: 299 Kudos [?]: 55 [0], given: 0 Re: The cost of a square slab is proportional to its thickness a [#permalink] 25 Nov 2013, 02:01 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. _________________ Intern Joined: 04 Jan 2012 Posts: 30 Location: Malaysia GMAT 1: 740 Q48 V42 WE: Analyst (Consulting) Followers: 5 Kudos [?]: 51 [0], given: 12 Re: The cost of a square slab is proportional to its thickness a [#permalink] 29 May 2014, 00:44 It would be easier to say that: Cost is proportional to the volume or m^3? (which is essentially what Width x Height x Thickness is) So for: 1) (Vol1 - Vol2)X = 160 X = 400 : (cost per m^3) Sufficient, can find for volume of 3 x 3 x 0.1 2) Same rationale. Sufficient Intern Joined: 05 Jan 2015 Posts: 17 Followers: 0 Kudos [?]: 1 [0], given: 3 Interpreting the infamous stone slab word problem [#permalink] 17 Jan 2015, 17:50 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 2 meters 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 meters 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

I read over this on multiple forums and have come to understand why the correct answer is correct.

That is this question can be written as C = kAT where C is cost, A is area, and T is thickness. The wording of the problem essentially states that C is jointly proportional to A and T.

I (and I think a few others) chose to interpret the question as C = kA + mT, where there are now two proportionality constants defining the relationship. At first glance this seems like what the question is leading into, but alas is not the OA.

So based on the original wording of the question we can surmise the relationship is C=kAT. But what wording do you use then to describe the second relationship C = kA + mT? This way I know how to distinguish between these two types of relationships described.
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Re: Interpreting the infamous stone slab word problem [#permalink]  18 Jan 2015, 00:17
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Kevin,
In the case you mentioned, the wording should be something like
"The cost of stone slab is dependent on its area and height"
this can be interpreted as "C= kA + mT

But when it is mentioned that cost is "proportional" to any particular factor, then that implies a multiplicative relation only.

Further, on a lighter note: in the relation C= kA+mT; there can still be a cost even when one of A or T is zero!!
So, I feel that even this fact indicates toward a relation like C= kAT

Hope it helps!
Re: Interpreting the infamous stone slab word problem   [#permalink] 18 Jan 2015, 00:17

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