The cost of a square slab is proportional to thickness and also proportional to the square of its length. What is the cost of a square slab that is 3 m long and 0.1 m 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 meter thick
(2) The cost of a square slab that is 3 meters long and 0.1 meters thick is 300 more than the cost of a square slab that is 3 meters long and 0.1 meter thick

Answer is D.

I chose B... Confused. Does proportional imply a cost relationship at the same ratio as length or thickness? For example, a square slab of length L costs kL, hence the ratio of cost between two slabs of lengths La = 2 and Lb =3 is 2:3? Could someone help me with the formula translation. Thanks.

The description of how cost is proportionate to length and thickness can be converted to an equation as follows:

Cost = k x Square(Length) x Thickness, where k is a constant.

We are now asked to find the cost, for a slab of given length and thickness. In order to find the cost, we need to determine the constant "k".

Statement (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 meter thick

So that means k x Square(2) x 0.2 = k x Square(2) x 0.2 + $160
From the above equation you can determine "k". So we can plug this in the equation to find the cost of the 3 meter long slab. HENCE SUFFICIENT.

Statement (2): The cost of a square slab that is 3 meters long and 0.1 meters thick is 300 more than the cost of a square slab that is 3 meters long and 0.1 meter thick. The above statement is very similar to Statement (1), except for the difference in dimensions and costs. So this statement is also SUFFICIENT to determine the cost.

Hence answer is (D).

I am not sure why you square the length. I don't think this is correct.

Ignore my previous comment. I know reread the question. Thanks.

Sorry but is statement 2 correct?

(2) The cost of a square slab that is 3 meters long and 0.1 meters thick is 300 more than the cost of a square slab that is 3 meters long and 0.1 meter thick

how a slab that is identical is going to be 300$ more? The lenght and the thickness is the same for both slabs, isn´t it?

I guess I´m missing something

Thanks

Harish, well done on the explanation.

Luci, that has to be a typo in (2), but it threw me off, too.

Borcho, can you please clarify the dimensions given in (2) for future forum users?

Thanks all!

The cost of a square slab is proportional to thickness and also proportional to the square of its length. What is the cost of a square slab that is 3 m long and 0.1 m 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 meter thick
(2) The cost of a square slab that is 2 meters long and 0.1 meters thick is 300 more than the cost of a square slab that is 3 meters long and 0.1 meter thick

Answer is D.