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.

I read this question wrong. I was thinking that the cost was different for the length vs the thickness..... thx..

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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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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Correct.
Thank u.
Dont know in what i was thinking about!

D is the one
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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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Please +1 KUDO if my post helps. Thank you.

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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Thanks & Regards,
Anaira Mitch