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

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Manager
Joined: 18 Jun 2007
Posts: 67
The cost of a square slab is proportional to its thickness a [#permalink]

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19 Jul 2008, 21:29
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62% (01:43) correct 38% (00:51) wrong based on 397 sessions

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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: 938 Re: The cost of a square slab is proportional to its thickness a [#permalink] ### Show Tags 19 Jul 2008, 21:47 5 This post received KUDOS 6 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: 67 Re: The cost of a square slab is proportional to its thickness a [#permalink] ### Show Tags 19 Jul 2008, 21:55 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: 324 Re: The cost of a square slab is proportional to its thickness a [#permalink] ### Show Tags 19 Jul 2008, 21:56 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
(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. Current Student Status: Everyone is a leader. Just stop listening to others. Joined: 22 Mar 2013 Posts: 962 Location: India GPA: 3.51 WE: Information Technology (Computer Software) Re: The cost of a square slab is proportional to its thickness a [#permalink] ### Show Tags 09 Sep 2013, 07:04 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: 39589 Re: The cost of a square slab is proportional to its thickness a [#permalink] ### Show Tags 10 Sep 2013, 01:38 _____________ Merging similar topics. _________________ Intern Joined: 18 Aug 2013 Posts: 18 Re: The cost of a square slab is proportional to its thickness a [#permalink] ### Show Tags 11 Sep 2013, 05:12 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: 878 Re: The cost of a square slab is proportional to its thickness a [#permalink] ### Show Tags 27 Oct 2013, 03:32 1 This post received KUDOS 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 http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html GMAT Club Legend Joined: 09 Sep 2013 Posts: 15916 Re: The cost of a square slab is proportional to its thickness a [#permalink] ### Show Tags 25 Nov 2013, 03:01 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 GMAT 1: 740 Q48 V42 WE: Consulting (Consulting) Re: The cost of a square slab is proportional to its thickness a [#permalink] ### Show Tags 29 May 2014, 01:44 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: 13 Interpreting the infamous stone slab word problem [#permalink] ### Show Tags 17 Jan 2015, 18:50 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.
Intern
Joined: 09 May 2013
Posts: 15
Re: Interpreting the infamous stone slab word problem [#permalink]

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18 Jan 2015, 01:17
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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, 01:17

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