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

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

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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 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 meter 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 meter thick.

OA D

Source: GMAT Prep

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BTGmoderatorDC 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 square slab that is 3 meters long and 0.1 meter thick?

(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 meter 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 meter thick.

OA D

Source: GMAT Prep
Say the cost of the slab is C, thickness is T and length is L.

It is given C is proportional to T and square of L. Say a constant is K.

Thus, C = KTL^2

We are given that T = 0.1 meter, and L = 3 meters

Thus, C = K*0.1*3^2

C = 0.9K

If we get the value of K, we get the answer.

Question rephrased: What's the value of K?

Let's take each statement one by one.

(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 meter thick.

Slab #1: Values given for L1, and T1. Value of C1 not given.
Slab #2: Values given for L2, and T2. Value of C2 not given.

Say C' = Difference of C1 and C2

C' = K*T1*(L1)^2 - K*T2*(L2)^2
C' = K[T1*(L1)^2 - T2*(L2)^2]

We know that values of C', L1, T1, T2 and L2; thus, the value of K can be calculated. Sufficient.

(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.

It's the same as Statement 1. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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BTGmoderatorDC 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 square slab that is 3 meters long and 0.1 meter thick?

(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 meter 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 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.

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