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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] New post 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
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Re: The cost of a square slab is proportional to its thickness a [#permalink] New post 19 Jul 2008, 20:47
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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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Re: The cost of a square slab is proportional to its thickness a [#permalink] New post 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..
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Re: The cost of a square slab is proportional to its thickness a [#permalink] New post 19 Jul 2008, 20:56
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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
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Re: The cost of a square slab is proportional to its thickness a [#permalink] New post 07 Sep 2009, 11:46
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Re: The cost of a square slab is proportional to its thickness a [#permalink] New post 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.
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Re: The cost of a square slab is proportional to its thickness a [#permalink] New post 07 Sep 2009, 12:46
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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
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Re: The cost of a square slab is proportional to its thickness a [#permalink] New post 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.
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Re: The cost of a square slab is proportional to its thickness a [#permalink] New post 07 Sep 2009, 14:06
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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 a [#permalink] New post 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
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Re: The cost of a square slab is proportional to its thickness a [#permalink] New post 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
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Re: The cost of a square slab is proportional to its thickness a [#permalink] New post 19 Jan 2013, 02:01
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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 a [#permalink] New post 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 a [#permalink] New post 10 Sep 2013, 00:38
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Re: The cost of a square slab is proportional to its thickness a [#permalink] New post 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 a [#permalink] New post 27 Oct 2013, 02:32
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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 a [#permalink] New post 25 Nov 2013, 02:01
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Re: The cost of a square slab is proportional to its thickness a [#permalink] New post 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
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Interpreting the infamous stone slab word problem [#permalink] New post 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] New post 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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