Data Sufficiency

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 slab that is 3 meters long and .1 meter thick?

A.) the cost of a slab that is 2 meters long and .2 meters thick is $160 more than the cost of a slab that is 2 meters long and .1 meters thick

B.) the cost of a slab that is 3 meters long and .1 meters thick is $200 more than the cost of a square slab that is 2 meters long and .1 meters thick


OA after a few responses.

I am just guessing here..

Using the formula of TSA : 2(lw + wh + hl)

(D)

That is correct. I would appreciate if someone could elaborate.

The question tells you that C=k*t*l^2
Where C=cost, k=coefficient of proportionality (what you need to find), t-thickness,l-length.

So, 1. tells us that k*0.2*4 - k*0.1*4 = 160------> k = 400
Using this information we can find the Cost of the slab in the original q--->
C=400*0.1*9 = 360

Same goes for 2. ----> k*0.1*9 - k*0.1*4 = 200----> k = 400
Answer to question c = 400*0.1*9 = 360

This is why our answer is D

Thanks lilu! Great Explanation.

mike22629 wrote: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 slab that is 3 meters long and .1 meter thick?

A.) the cost of a slab that is 2 meters long and .2 meters thick is $160 more than the cost of a slab that is 2 meters long and .1 meters thick

B.) the cost of a slab that is 3 meters long and .1 meters thick is $200 more than the cost of a square slab that is 2 meters long and .1 meters thick


OA after a few responses.

Nice question, but can please write "0.1" instead of ".1". I am pretty sure GMAT respects the decimal by placing "0" in front of decimal.

c = k * s * t^2, where k = constant, s = length, t = thickness
c = ?, when s=3, t=0.1

(i) c=k * (2) * (0.2)^2 = 0.08 * k
c=k * (2) * (0.1)^2 = 0.02 * k

(0.08 * k) - (0.02 * k) = 160
0.06 * k = 160
k = 160 * 100 / 6

Subst. value of k in -
Suff

(ii) Same as (i) with diff. values.
Suff.

Hence [spoiler][D][/spoiler]