A rectangular wall is completely filled with square tiles of

Question

A rectangular wall is completely filled with square tiles of 9 rows and 13 columns. The tiles are of equal area. Each tile is yellow or orange, and no tiles with a common side are the same color. If the wall contains more yellow tiles than orange tiles, how many yellow tiles does the wall contain?

A. 57
B. 58
C. 59
D. 60
E. 61

A. 57
B. 58
C. 59
D. 60
E. 61

Bunuel · Answer

In order to meet the conditions that no tiles with a common side are the same color and that the wall contains more yellow tiles than orange tiles, the wall should look like as follows: Tiles.png Now, 8 rows contain the same number of yellow and orange tiles and the last one contains one more yellow tile, thus the total number of yellow tiles is one more than the total number of orange tiles. Since, the total number of tiles is 9*13=117, then (yellow)+(yellow-1)=117 --> 2*(yellow)=118 --> (yellow)=59. Answer: C. Hope it's clear.

gmatbull · Answer

Hello Bunuel,
thanks for the prompt response as usual and ur feedback have kept quite a lot of members
faithful to the forum.

I actually drew the pattern for only 3 columns; thereafter, a said 7*5 + 6*4 = 59 yellows
meaning 7 yellows in 5 cols Plus 6 yellows in 4 cols

But drawing the diagram could be cumbersome. What do you think?

Bunuel · Answer

Well, yes. I just draw it to illustrate.

PareshGmat · Answer

If we group a pattern of 18 tiles, yellow tiles = orange tiles = 9

First 9 have yellow = 5, orange = 4 ............... (1)

Next 9 have yellow = 4, orange = 5 ................. (2) and so on........

Attachment:

Tiles.png [ 5.26 KiB | Viewed 3149 times ]

Total tiles required = 13*9 = 117

Nearest divisible to 117 is 108

Out of 108 tiles, 54 are orange & 54 are yellow

Remaining 9 will have yellow = 5 .............. From (1)

Total yellow = 54+5 = 59

Answer = C

m1m4p43 · Answer

Another way to solve this interesting question.

As number of yellow tiles is more than orange tiles and no same color tile is next to one another and the wall is a 9x13 area.

The wall first column should start by a yellow tile on the top àn end by another yellow at the bottom. Therefore, there are 5 yellow tiles on the first column.

As no same color tile is next to one another, the second row should start and end with orange ones, which means 4 yellow tiles and so on.

Total number of yellow tiles = 7x5 + 6x4 = 59. Choice C.

Posted from my mobile device

bumpbot · Answer

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A rectangular wall is completely filled with square tiles of

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