I think the answer is B- 388.
First we find out how much it costs to paint per surface area of the cube, which will be price/total surface area.
Price = 92
Total Surface Area= 2(80*100) + 2(80*160) + 2(100*160)= 73,600
Therefore price per surface area = 92/73600
Next, we are told that it is cut into several identical cubes of the largest size, and so to determine the dimensions of this cube we just take the greatest common factor of 80,100 & 160, which is 20. Therefore each cube will have dimensions 20*20*20.
Given this information, we can re-label the cuboid as having dimensions 4*5*8, so we can say there are a total of 4*5*8=160 identical cubes.
Now, there are some cubes in the middle of the cuboid which haven't been painted at all. To find out this number, imagine you are 'peeling off' the outer layer of cubes leaving inside only the cubes in the middle.
This will be (4-2)*(5-2)*(8-2)=2*3*6= 36 cubes.
Therefore we have to paint each side of the cube for all these 36 cubes.
This gives us a surface area of painting of: 36*6*20*20= 86,400
Now we are able to only concentrate on the outer layer of cubes. Notice that the cubes on the edges of the cuboid will have 3 sides of them painted, so for these cubes, we only need to paint an additional 3 sides. Since there are 8 edges, this gives us:
8*3*20*20=9,600
Now we have 116 cubes left to be dealt (160-8-36)
Notice that on the sides of the cube, these cubes will have been painted on 2 sides already, so we only need to paint an additional 4 sides for these cubes but we must not include the cubes at the edges.
The number of these cubes are (2*4)+(3*4)+(6*4)=44.
So surface area of painting is 44*4*20*20=70,400
We now have 116-44=72 cubes left. These cubes have only been painted on one side. So we need to paint 5 sides of each of these cubes.
Surface area of painting for these cubes is 72*5*20*20=144,000
We are now finished. The total additional surface area of painting we have had to do is the sum of all of these, i.e.
86,400+9,600+70,400+144,000= 310,400
So the price we pay is = (price per surface area) * (surface area of painting)
Therefore, price = (92/73,600) * (310,400) = 388.
If someone knows of a much quicker way to solve this then please post it, also could you please confirm if this is the correct answer? Also out of interest, was this a GMAT question? I hope not, as there is no way I would have been able to do this in 2 mins lol... Thanks....
Featured Course
