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

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Difficulty:   55% (hard)

Question Stats: 63% (01:50) correct 37% (01:57) wrong based on 356 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 0.1 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.

Attachment: DS.jpg [ 91.34 KiB | Viewed 8340 times ]

Originally posted by TNTGMAT on 19 Jul 2008, 21:29.
Last edited by Bunuel on 21 Feb 2019, 05:38, edited 2 times in total.
Renamed the topic and edited the question.
Director  Joined: 10 Sep 2007
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Re: The cost of a square slab is proportional to its thickness and also  [#permalink]

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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.
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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 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
Senior Manager  Joined: 18 Jun 2009
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Re: The cost of a square slab is proportional to its thickness and also  [#permalink]

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Stmt1 - 2m long by 0.2m thick is $160 more than 2m long by 0.1m thick Now since the cost is directly porportional to the thickness. Lets imagine the "2m long by 0.2m thick" slab as two "2m long by 0.1m thick" slabs we have "2m long by 0.2m thick" = 160 + "2m long by 0.1m thick" "2m long by 0.2m thick" can be written as "2m long by 0.1m thick" + "2m long by 0.1m thick" therefore "2m long by 0.1m thick" + "2m long by 0.1m thick" = 160 + "2m long by 0.1m thick" therefore "2m long by 0.1m thick" =$160 .... 1

We cant deduce from stmt 1 ... insuff

Stmt 2) 3m long by 0.1m thick is $200 more than 2m long by 0.1m thick 3m long by 0.1m thick =$200 + 2m long by 0.1m thick .... 2

stmt2 insuffecient

combing 1 and 2

we have 3m long by 0.1m thick = $200 +$160(from 1)

(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. Director  Status: Everyone is a leader. Just stop listening to others. Joined: 22 Mar 2013 Posts: 710 Location: India GPA: 3.51 WE: Information Technology (Computer Software) Re: The cost of a square slab is proportional to its thickness and also [#permalink] Show Tags 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". Intern  Joined: 18 Aug 2013 Posts: 13 Re: The cost of a square slab is proportional to its thickness and also [#permalink] Show Tags 1 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: 687 Re: The cost of a square slab is proportional to its thickness and also [#permalink] Show Tags 1 1 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=> $$X (0.1) (3^2) - X (0.1) (2^2) = 200$$=> $$X=400$$ Intern  Joined: 05 Jan 2015 Posts: 11 Re: The cost of a square slab is proportional to its thickness and also [#permalink] Show Tags 1 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
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Re: The cost of a square slab is proportional to its thickness and also  [#permalink]

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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!
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Re: The cost of a square slab is proportional to its thickness and also  [#permalink]

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cost of slab=(l^2)*t*k where k is the constant of proportionality.
we need this k to be able to arrive at the cost.

1) 4*0.2*k=4*0.1*k+160
=>4*0.1*k=160

we can solve for k, the proportionality constant and compute the cost of the slab in the stimulus.
sufficient

2) 9*0.1*k-4*0.1*k=200
=>0.1k(9-4)=200
=>k=200/(5*0.1)
we can compute the cost of the given slab in the stimulus.
sufficient

hence D
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Re: The cost of a square slab is proportional to its thickness and also  [#permalink]

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CoolKevin 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 0.1m 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.

The problem is that you are using the incorrect Formula: It is not C = kA + mT, but C = kA x mT (Volume). Then altogether becomes C= kmAT, the constants k and m can be multiplied and form a single constant C = (km)AT.
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Re: The cost of a square slab is proportional to its thickness and also  [#permalink]

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cledgard wrote:
The problem is that you are using the incorrect Formula: It is not C = kA + mT, but C = kA x mT (Volume). Then altogether becomes C= kmAT, the constants k and m can be multiplied and form a single constant C = (km)AT.

How do you know that the formula needs to be volume? I understand how that would make sense in real life, but I don't see anything in the question that would indicate that.
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Re: The cost of a square slab is proportional to its thickness and also  [#permalink]

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gmatman1031 wrote:
How do you know that the formula needs to be volume? I understand how that would make sense in real life, but I don't see anything in the question that would indicate that.

The definition of proportionality (found here and here) dictates this. Also, since this question deals with joint proportionality, I found this helpful as well.

grant1377 wrote:
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.

Yes. According to this Wikipedia article: "If the term proportional is connected to two variables without further qualification, generally direct proportionality can be assumed." Re: The cost of a square slab is proportional to its thickness and also   [#permalink] 12 Feb 2019, 18:13
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