DS with Ratios

[susan.meng]

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 meters thick?
1. the cost of a square slab that is 2 meters long and 0.2 meters thick is $160 more than the cost of a square slab that is 2 meters long and 0.1 meters 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 meters thick

What is a standard way to approach problems like this?

[supratims]

Given that the cost of a square slab is proportional to its thickness and also proportional to the square of its length.
Its cost, C can be written as
C = k (W) (L) (L) (note that L is twice because cost is proportional to square of the length.)
Here k is a constant.
We need to find C, when W = 0.1, and L = 3 ;
C=k (0.1) (3) (3) = k(0.9) ;
So knowing k will give us the cost.

From 1)
When W = 0.2, and L = 2. Cost C1 = k (0.2) (2) (2)
also When W = 0.1 and L = 2, Cost C2 = k (0.1) (2) (2)
Also C1 - C2 = 160 ; this will give us value of k, the constant. Hence the answer.
So 1) is sufficient

From 2) On similar lines, we can get k from 2) as well.

So 1) and 2) alone are sufficient. So answer is D)

What is the official answer ?

[Ben Ku]

Nice work, supratim; your answer is correct.

The first step is to rephrase the question, as supratim correctly did. If y is directly related to x, then we can write it y = kx.

Here, C = k(T)(L^2). Since we know what T and L are, to find the cost, we just need to know k. Our rephrase is: what is k?

Each of the statements gives us the same information. So either both of them separately will help us answer the question (D), or neither of them works (E).

Each of the statements provides the difference between the costs. Let's take statement 1:
C1 - C2 = 160; k(T1)(L1)^2 - k(T2)(L2)^2 = k[T1 x L1^2 - T2 x L2^2] = 160
Since T1, T2, L1, and L2 are given, then it is clear that we can find k, so statement 1 is sufficient. in the same way, statement 2 is also sufficeint.

I hope that helps.