Problem Solving

BTGmoderatorLU wrote: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

. . . and no tiles with a common side are the same color
To meet this condition, it MUST be the case that the yellow and orange squares are arranged in a checkerboard pattern.
In such a checkerboard pattern, the colors alternate yellow, orange, yellow, orange, yellow, orange etc
This means half of the squares are orange and half are yellow.
HOWEVER, the wall has 9 rows and 13 columns, which means the TOTAL number of tiles = (9)(13) = 117
This is an odd number, so there will be one extra tile.

. . . the wall contains more yellow tiles than orange tiles
So, there must be one extra YELLOW tile.
Let x = number of orange tiles
So, x+1 = number of yellow tiles

There are 117 tiles, so we can write: x + (x + 1) = 117
Simplify: 2x + 1 = 117
Solve, x = 58
So, there are 58 orange tiles and 59 yellow tiles.

Answer: C

Cheers,
Brent