The cost of a square slab is proportional to its thickness and also

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

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

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!

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.

This is a question on the concept of Proportionality. Note that in questions related to this concept, there will always be a constant called the constant of proportionality which is required to convert the proportionality expression to an equation.

The cost of the slab, c, is proportional to its thickness, t, and also proportional to the square of its length viz., \(l^2\) i.e.
c ∝ t * \(l^2\).

To convert the above expression to an equation, we introduce a constant of proportionality, say k. Therefore,
c = k*t\(l^2\).
We need to find the cost of a square slab of length 3 meters and of thickness 0.1 meters. Effectively, we need to find the value of c when t = 0.1 and l = 3, for which we need the value of k.

From statement I alone, we know the difference in the costs of two slabs whose dimensions are given.
This is sufficient to develop an equation containing k and to solve for k. Statement I alone is sufficient.

If c1 = k * 0.2*4 and c2 = k* 0.1*4, we know c1= c2 +160. This is sufficient to find the value of k.
Since statement I alone is sufficient, answer options B, C, and E can be eliminated. Possible answer options are A or D.

From statement II alone, we know the difference in the costs again and we have already done something similar in statement I. So, time to SAVE TIME and conclude that statement II alone is sufficient instead of trying to work out the equations.
Statement II alone is sufficient. Answer option A can be eliminated.

The correct answer option is D.
Whenever the opportunity to save time presents itself, grab it with both hands. And do not forget that a lot of DS questions actually present you with such opportunities, if only you are ready to take them.

Hope that helps!
Arvind.

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.