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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 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

(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
[Reveal] Spoiler: OA
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Re: DS - square slab [#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: DS - square slab [#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: DS - square slab [#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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Proportionality (Disagree with OA) [#permalink] New post 07 Sep 2009, 11:46
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Re: Proportionality (Disagree with OA) [#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)

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Re: Proportionality (Disagree with OA) [#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: Proportionality (Disagree with OA) [#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: Proportionality (Disagree with OA) [#permalink] New post 07 Sep 2009, 14:06
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: Proportionality (Disagree with OA) [#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: Proportionality (Disagree with OA) [#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 [#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 [#permalink] New post 10 Sep 2013, 00:38
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Re: The cost of a square slab is proportional to its thickness [#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 [#permalink] New post 27 Oct 2013, 02:32
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: Proportionality (Disagree with OA) [#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
Re: The cost of a square slab is proportional to its thickness a   [#permalink] 29 May 2014, 00:44
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