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The cost of a square slab is proportional to its thickness and also
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Updated on: 21 Feb 2019, 05:38
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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:
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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.




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Re: The cost of a square slab is proportional to its thickness and also
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19 Jul 2008, 21:47
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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Re: The cost of a square slab is proportional to its thickness and also
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19 Jul 2008, 21:56
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



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Re: The cost of a square slab is proportional to its thickness and also
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21 Jul 2009, 15:59
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)
= $360 ...
therefore answer is C
Please confirm



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Re: The cost of a square slab is proportional to its thickness and also
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21 Jul 2009, 16:02
Thickness = t Length = l \(c = 9*0.1*k = ?\) "and also proportional" means that we can put both in the same formula: \(Cost = k*t*l^2\), where k is a constant 1) \(k*2^2*0.1\) costs x \(k*2^2*0.2\) costs x + 160 Using rule of three (crossmultiplication): \((k*2^2*0.1)/(k*2^2*0.2)= x/( x + 160 )\), you can find x, and then do the same with 9*0.1*k SUFFICIENT 2) Using the same reasoning of 1) SUFFICIENT Answer D PS.: It was worth? Consider a kudo...



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Re: The cost of a square slab is proportional to its thickness and also
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07 Sep 2009, 12:50
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.
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Re: The cost of a square slab is proportional to its thickness and also
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07 Sep 2009, 13:46
I think the cost function is the following:
\(C=k\times t\times l^2\) tthickness llength
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



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Re: The cost of a square slab is proportional to its thickness and also
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07 Sep 2009, 14:08
LenaA wrote: I think the cost function is the following:
\(C=k\times t\times l^2\) tthickness llength
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.
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Re: The cost of a square slab is proportional to its thickness and also
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07 Sep 2009, 15:06
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



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Re: The cost of a square slab is proportional to its thickness and also
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20 Dec 2009, 22:32
The key with such questions is to set up the formula based on the proportionality. Cost = K*(L^2)*T Where K is a constant L is the length T is the thickness Solving we get D Note is something is inversely proportional, divide instead of multiply. For example if the cost is inversely proportional to the square root of slab impurity then the above formula will become Cost = K*(L^2)*T/sqrt(I)
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Re: The cost of a square slab is proportional to its thickness and also
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19 Jan 2013, 03:01
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 and also
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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
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Re: The cost of a square slab is proportional to its thickness and also
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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



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Re: The cost of a square slab is proportional to its thickness and also
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27 Oct 2013, 03:32
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: The cost of a square slab is proportional to its thickness and also
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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.



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Re: The cost of a square slab is proportional to its thickness and also
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18 Jan 2015, 01:17
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
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04 Feb 2017, 04:02
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*k4*0.1*k=200 =>0.1k(94)=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
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18 Dec 2018, 07:38
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
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12 Feb 2019, 15:24
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
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12 Feb 2019, 18:13
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."




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