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Intern  Joined: 30 Mar 2015
Posts: 16
A certain rectangular wall is 12 feet high and 8 feet long.  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 66% (02:50) correct 34% (02:48) wrong based on 203 sessions

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A certain rectangular wall is 12 feet high and 8 feet long. It will be tiled with nonoverlapping square tiles that have sides of length 16 inches. The entire wall will be covered with tile and no tiles will be cut. Each tile consists of 16 smaller squares, each with sides of length 4 inches in the pattern shown in the diagram above. How many small blue squares will be on the wall? (1ft = 12 in)

a. 24
b. 216
c. 288
d. 864
e. 1,152

Attachments Screen Shot 2016-08-14 at 7.16.43 PM.png [ 27.55 KiB | Viewed 5440 times ]

Marshall & McDonough Moderator D
Joined: 13 Apr 2015
Posts: 1686
Location: India
Re: A certain rectangular wall is 12 feet high and 8 feet long.  [#permalink]

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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

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Senior SC Moderator V
Joined: 22 May 2016
Posts: 3536
A certain rectangular wall is 12 feet high and 8 feet long.  [#permalink]

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hennaj wrote:
A certain rectangular wall is 12 feet high and 8 feet long. It will be tiled with nonoverlapping square tiles that have sides of length 16 inches. The entire wall will be covered with tile and no tiles will be cut. Each tile consists of 16 smaller squares, each with sides of length 4 inches in the pattern shown in the diagram above. How many small blue squares will be on the wall? (1ft = 12 in)

a. 24
b. 216
c. 288
d. 864
e. 1,152

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

*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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Intern  B
Joined: 01 Jun 2017
Posts: 19
Re: A certain rectangular wall is 12 feet high and 8 feet long.  [#permalink]

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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
Intern  B
Joined: 25 Aug 2014
Posts: 1
A certain rectangular wall is 12 feet high and 8 feet long.  [#permalink]

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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.
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9695
Location: Pune, India
Re: A certain rectangular wall is 12 feet high and 8 feet long.  [#permalink]

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hennaj wrote:
A certain rectangular wall is 12 feet high and 8 feet long. It will be tiled with nonoverlapping square tiles that have sides of length 16 inches. The entire wall will be covered with tile and no tiles will be cut. Each tile consists of 16 smaller squares, each with sides of length 4 inches in the pattern shown in the diagram above. How many small blue squares will be on the wall? (1ft = 12 in)

a. 24
b. 216
c. 288
d. 864
e. 1,152

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

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