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.

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

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 (cross-multiplication): \((k*2^2*0.1)/(k*2^2*0.2)= x/( x + 160 )\), 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...

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

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

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
_________________

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

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.

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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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.