A certain rectangular wall is 12 feet high and 8 feet long.

Area of the rectangular wall = 12 * 8 = 96 sq.ft = 96 * 12 * 12 sq.inches

Area of each tile = 16 * 16 sq.inches

Number of tiles = (96 * 12 * 12)/(16 * 16) = 54

Each tile has 4 blue squares --> Number of blue squares = 54 * 4 = 216

Answer: B

Distraction: "Each tile consists of 16 smaller squares, each with sides of length 4 inches . . ."

Focus instead on the 16x16 tiles.

-- "each [large 16x16] tile" per the pattern in the diagram, has 4 smaller blue tiles.

-- find the number of large (16x16) tiles that will fit into the area of the wall. Multiply that number by 4 to get the number of blue tiles.

I converted and divided the way I did to avoid huge numbers.*

1) Convert feet to inches for wall height and length

Wall height = 12 feet =
12 feet * 12 inches/1foot = 144 inches

Wall length = 8 feet * 12 inches/foot = 96 inches

2)Calculate how many tiles will fit: Divide height and length of wall, respectively, by length of one side of a tile

Length of one side of a tile = 16 inches

So the height will have 144 in/16 in = 9 tiles (that will form 9 rows)

Length will have 96 in/16 in = 6 tiles (that will form 6 columns)

Total number of tiles is 9 * 6 = 54 tiles

3) How many blue tiles total?

There are 4 blue tiles on one big tile.
4 blue tiles * 54 big tiles = 216 blue tiles

Answer B

*I did not use these calculations when doing the problem, but here is the arithmetic with no "shortcuts":

Wall area (where 12 feet = 144 inches and 8 feet = 96 inches) --> 144 in * 96 in = 13,284 sq in
Tile area = 16 in * 16 in = 256 sq in

Wall area/tile area = # of tiles that will fit

13,284 sq in/256 sq in per tile = 54 tiles

54 tiles * 4 blue per tile = 216 blue
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total Height= 144 inch(12*12)
total width= 96 inch(12*8)

number of squares in one column= 144/16=9 squares
number of squares in one row= 96/16=6 squares

total squares= 9*6=54 squares

1 square has 4 blue sqaures. Therefore, total blue squares= 54*4=216

Ans. B

Visualize a rectangular wall with height of 12 feet = 144 inches and lenght 8 feet = 96 inches.

You have to insert square tiles, each of which are 16 inches long, into this rectangular wall.

Vertically you can insert 9 tiles and horizontally - 6 tiles. In total - 54 tiles. Each tile consists of 4 blue small square.

Finally you have 216 small blue squares.

Therefore, the correct answer will be - B.

Since 1/4th of each tile is blue, 1/4th of the entire wall will be blue.

Area of blue tiles = 12*8/4 = 24 feet^2

Since area of each blue square is 4 inch * 4 inch,

Number of blue tiles = 24 * 12 in * 12 in / 4 in * 4 in = 216

Answer (B)
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Area of the wall - 12 x 8 = 96 sq ft

Dimension of one tile is given as 16 inches

Given that, 1 ft = 12 inches
Therefore 1 inch = 1/12 ft

Converting dimension of one tile to feet - 16 x 1/12 = 4/3 ft

Area of 1 tile = 4/3 x 4/3 = 16/9 sq ft

Number of tiles required to cover the entire wall - 96 x 9/16 = 54 tiles

Each tile has 4 blue squares - 54 x 4 = 216 blue squares

(B)

Don't make the mistake I made which was to think all 16 small tiles were blue. No some of them are white, only 4 of them are blue per big tile. So the answer is 54*4 = 216 not 54*16 = 864

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