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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