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

Question

Harry is building his house. While constructing the staircase, he used 10 cuboid shape stone blocks. One side of each stone block was textured while all other sides were plain (or regular). He wants to keep all the textured surfaces at the surfaces which are exposed. If side ABCD and BCFE of the staircases are covered by the wall of the house and the ground respectively, what is the maximum possible ratio of the total exposed textured surfaces to the total exposed surfaces area of the staircase?

A. \(\frac{7}{22}\)

B. \(\frac{17}{52}\)

C. \(\frac{7}{18}\)

D. \(\frac{17}{36}\)

E. \(\frac{1}{2}\)

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Official Answer

C

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A.  \frac{7}{22}

B.  \frac{17}{52}

C.  \frac{7}{18}

D.  \frac{17}{36}

​E.  \frac{1}{2}

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ChandlerBong · Answer

Hi Experts Bunuel , ThatDudeKnows , KarishmaB , ScottTargetTestPrep , Can you please share your approach to this Geometry problem? Thanks in advance.

PerfectScores · Answer

The total exposed area is:

Left side: 5*5*10(squares) = 250
Right side: 5*5*10(squares) = 250
Top of the stairs: 5*10*4 = 200
Front of the stairs: 5*10*4 = 200

Total exposed area = 250 + 250 + 200 + 200 = 900

The trick to the question is that any side can be textured. For maximising area:

- texture the top of the stairs: 5*10*4 = 200
- For the remaining 6 blocks which were not included, texture the sides: 5*5*6 = 150

Total textured/exposed area = 150 + 200 = 350

Ratio = 350/900 = 7/18

ThatDudeKnows · Answer

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.

KarishmaB · Answer

Screenshot 2023-05-29 at 9.14.37 PM.png 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)

yaygmat · Answer

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

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

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