A rectangular wall is covered entirely with two kinds of decorative tiles: regular and jumbo. 1/3 of the tiles are jumbo tiles, which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles. If regular tiles cover 80 square feet of the wall, and no tiles overlap, what is the area of the entire wall?
A) 160
B) 240
C) 360
D) 440
E) 560
My approach:
Length of Regular tile = l
Width of Regular tile = w
So, length of Jumbo tile= 3l
width of jumbo tile = 3w
Total no. of tiles be x
2/3*x*l*w= 80
xlw=120
1/3*9*l*w= 3*(120)= 360
therefore, toata are of wall = 120 + 360 = 480
480 is not in the options.
What's wrong in this approach?
D
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To make the math easier, let all of the tiles be SQUARES.eitijan wrote:A rectangular wall is covered entirely with two kinds of decorative tiles: regular and jumbo. 1/3 of the tiles are jumbo tiles, which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles. If regular tiles cover 80 square feet of the wall, and no tiles overlap, what is the area of the entire wall?
A) 160
B) 240
C) 360
D) 440
E) 560
Regular tiles:
Let each regular square tile have a side of 1, implying that the area of each regular square tile = 1² = 1.
Since regular tiles cover 80 square feet, the total number of regular tiles = (total regular tile area)/(area of each regular tile) = 80/1 = 80 regular tiles.
Jumbo tiles:
Since the length of a jumbo tile is 3 times the length of a regular tile, let each jumbo square tile have a side of 3, implying that the area of each jumbo square tile = 3² = 9 square feet.
Since 1/3 of the tiles are jumbo, of every 3 tiles, 1 is a jumbo, while 2 are regular.
Thus, the number of jumbo tiles is 1/2 the number of regular tiles:
(1/2) * 80 = 40 jumbo tiles.
Since there are 40 jumbo tiles, each with an area of 9 square feet, the total area covered by the jumbo square tiles = 40*9 = 360 square feet.
Thus:
Area of the entire wall = (regular tile area) + (jumbo tile area) = 80+360 = 440.
The correct answer is D.
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In your solution:eitijan wrote: My approach:
Length of Regular tile = l
Width of Regular tile = w
So, length of Jumbo tile= 3l
width of jumbo tile = 3w
Total no. of tiles be x
2/3*x*l*w= 80
xlw=120
x = the total number of tiles covering the wall
lw = the area of each regular tile
As a result:
xlw = (total number of tiles covering the wall)(area of each regular tile)
Error:
The resulting product -- 120 square feet -- represents the area of the wall IF ALL OF THE TILES ARE REGULAR TILES.
Since ONLY 2/3 of the tiles are regular tiles, the resulting product does not correspond to the information in the prompt.
Fix:
You have correctly determined that the area covered by the jumbo tiles = 360 square feet.
Since the prompt indicates that the area covered by the regular tiles = 80 square feet, the total area of the wall = 360+80 = 440 square feet.
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Hi eitijan,
This question is loaded with little details. You'll need to take lots of notes, stay organized and do some basic math to get the correct answer.
We're told that there are two types of tiles: REGULAR and JUMBO.
Now come all of the little math facts you have to take note of (and deduce).....
1) 1/3 of the tiles are JUMBO tiles.
Since 1/3 are JUMBO, the other 2/3 are REGULAR.
This means that the ratio of JUMBO:REGULAR = 1:2; in other words, there are twice as many REGULAR tiles as JUMBO tiles.
2) JUMBO tiles have a length that is 3 TIMES that of the REGULAR tiles AND has the same ratio of length:width as the REGULAR tiles.
We'll come back to this information in a moment.
3) REGULAR tiles cover 80 square-feet of the wall.
Since we weren't given any information about the dimensions of the REGULAR tiles, we can TEST VALUES. Let's say....
1 REGULAR tile = 1ft x 1ft.
Since REGULAR tiles cover 80 square feet, that means there are 80 REGULAR tiles.
Now, let's go back to the 2nd piece of information.....
JUMBO TILES have 3 times the length and the same ratio of length:width as REGULAR tiles.
1 REGULAR tile = 1ft x 1ft.
1 JUMBO tile = 3ft x 3ft.
NOW, let's go back to the 1st piece of information.....
The ratio of JUMBO:REGULAR = 1:2
80 REGULAR tiles (each 1ft x 1ft)
40 JUMBO tiles (each 3ft x 3ft).
Total area of the wall = 80(1)(1) + 40(3)(3) = 80 + 360 = 440 square feet
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
This question is loaded with little details. You'll need to take lots of notes, stay organized and do some basic math to get the correct answer.
We're told that there are two types of tiles: REGULAR and JUMBO.
Now come all of the little math facts you have to take note of (and deduce).....
1) 1/3 of the tiles are JUMBO tiles.
Since 1/3 are JUMBO, the other 2/3 are REGULAR.
This means that the ratio of JUMBO:REGULAR = 1:2; in other words, there are twice as many REGULAR tiles as JUMBO tiles.
2) JUMBO tiles have a length that is 3 TIMES that of the REGULAR tiles AND has the same ratio of length:width as the REGULAR tiles.
We'll come back to this information in a moment.
3) REGULAR tiles cover 80 square-feet of the wall.
Since we weren't given any information about the dimensions of the REGULAR tiles, we can TEST VALUES. Let's say....
1 REGULAR tile = 1ft x 1ft.
Since REGULAR tiles cover 80 square feet, that means there are 80 REGULAR tiles.
Now, let's go back to the 2nd piece of information.....
JUMBO TILES have 3 times the length and the same ratio of length:width as REGULAR tiles.
1 REGULAR tile = 1ft x 1ft.
1 JUMBO tile = 3ft x 3ft.
NOW, let's go back to the 1st piece of information.....
The ratio of JUMBO:REGULAR = 1:2
80 REGULAR tiles (each 1ft x 1ft)
40 JUMBO tiles (each 3ft x 3ft).
Total area of the wall = 80(1)(1) + 40(3)(3) = 80 + 360 = 440 square feet
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
