Harry is building his house. While constructing the staircase, he used

ChandlerBong

My approach is to avoid the multiplication, not bother getting too elegant, and simply count.

Imagine how you could use 5x5 tiles to cover the entire exposed surface area. You'd need 1 to cover each end and you'd need 2 to cover each top and front. There are 10 exposed ends on each side of the staircase, so that's 20 tiles. Two for each top is 8 and 2 for each front is 8. 20+8+8 is a total of 36 congruent squares to cover the entire exposed surface area.

Now we need to see how many of those squares we'd want to have be textured. Look at the top step; which surface would you want to have be textured? Either the top or the front. The same would be true for the other 3 steps. So that's 2 squares per step times 4 steps, which equals 8 squares. From the other 6 cuboids, we can only make 1 end textured, so that's another 6 squares. 8+6 = 14.

14 textured; 36 total --> 14/36 = 7/18

Answer choice C.

The 6 blocks with orange ticks have no longer faces exposed. The only exposed faces are the two 5*5 faces on either side. Hence the textured area will be 25 the total exposed area is 50.

The 4 blocks with blue ticks have 4 faces exposed, 2 which are 10*5 in area and 2 which are 5*5 in area. This is total exposed area of 50 + 50 + 25 + 25 = 150 and the maximum textured area could be 50.

Total textured area = 25 * 6 + 4 * 50 = 350
Total exposed area = 50*6 + 150*4 = 900

Percentage = 35/90 = 7/18

Answer (C)

ScottTargetTestPrep do we see such questions in the GMAT? If yes, where can I find it on the TTP course?