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.

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

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

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...

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.

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.

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

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)

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

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

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

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=> \(X (0.1) (3^2) - X (0.1) (2^2) = 200\)=> \(X=400\)

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.

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!

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
_________________

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.

The definition of proportionality (found here and here) dictates this. Also, since this question deals with joint proportionality, I found this helpful as well.


Yes. According to this Wikipedia article: "If the term proportional is connected to two variables without further qualification, generally direct proportionality can be assumed."