Data Sufficiency

Hi

Need some help figuring out the below question

Question
The cost of a square slab is proportional to the square of its length and also proportional to its thickness.

What is the cost of a square slab that is 3m long and 0.1m thick?

1) Cost of square slab that is 2m long and 0.2m thick is $160 more than the cost of a square slab that is 2m long and 0.1m thick

2) Cost of square slab that is 3m long and 0.1m thick is $200 more than the cost of a square slab that is 2m long and 0.1m thick

Thanks

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 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 meters thick.

2) The cost of 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.

x is directly proportional to y implies the following:
x/y = k.
x = ky.
In each case, k is a CONSTANT.

The cost of a square slab is proportional to its thickness and also proportional to the square of its length.
Thus:
c = k * T * L².

What is the cost of a square slab that is 3 meters long and 0.1 meter thick?
Since c = k * T * L², we get:
c = k * 0.1 * 3²
c = 0.9k.
To determine the value of c, we need to know the value of k.

Question rephrased: What is the value of k?

Statement 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 meters thick.
Cost of a square slab that is 2 meters long and 0.2 meter thick = k * 0.2 * 2² = .8k.
Cost of a square slab that is 2 meters long and 0.1 meter thick = k * 0.1 * 2² = .4k.
Since the difference in cost is $160, we get:
0.8k - 160 = 0.4
0.4k = 160
k = 160/0.4 = 1600/4 = 400.
SUFFICIENT.

Statement 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.
Cost of a square slab that is 3 meters long and 0.1 meter thick = k * 0.1 * 3² = .9k.
Cost of a square slab that is 2 meters long and 0.1 meter thick = k * 0.1 * 2² = .4k.
Since the difference in cost is $200, we get:
0.9k - 200 = 0.4k
0.5k = 200
k = 200/0.5 = 2000/5 = 400.
SUFFICIENT.

The correct answer is D.

Thanks for the quick response. Appreciate it.

Binara

Hi Mitch,

Just to clarify on the wording. When the question says "cost of a square slab is proportional to its thickness and also proportional to the square of its length" can you go with the assumption that the constant of proportionality - in this case k - is the the same for both T & L?

c = k * T * L².

How would the wording be if the constant for proportionality were different for T & L in relation to total cost.

Thanks, Binara

Thanks for the quick response. Appreciate it.

Binara