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
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The cost of a square slab is proportional to its thickness a
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x is directly proportional to y implies the following: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/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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Say the cost of the slab is C, thickness is T and length is L.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
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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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