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Number of square tiles needed to cover a space on a wall of 72 x 108

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Carcass
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Number of square tiles needed to cover a space on a wall of 72 x 108 [#permalink] New post   Updated on: 16 Sep 2022, 07:59
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Quantity A
Quantity B
Number of square tiles needed to cover a space on a wall of 72” x 108”, using tiles that each have a perimeter of 36 inches.
Number of square tiles needed to make a rectangular border one tile wide around the outside of the same 72” x 108” space, using tiles that each have an area of 9 square inches.



A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

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Official Answer
B

Originally posted by Carcass on 06 Aug 2022, 00:41.
Last edited by Carcass on 16 Sep 2022, 07:59, edited 1 time in total.
Fixed OA
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Re: Number of square tiles needed to cover a space on a wall of 72 x 108 [#permalink] New post   08 Aug 2022, 05:01
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Re: Number of square tiles needed to cover a space on a wall of 72 x 108 [#permalink] New post   03 Sep 2022, 03:01
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For Quantity 1... Perimiter of tile is 36 so each side measures 9.. So area is 81...no of tiles required is 72*108/81=96

For Quantity 2...Area of tile is 9 so each side is 3..Now they are putting one tile extra on every side to increase width..Width is 72..So tiles required for one side is 72/3=24..Total 48 for two sides

hence A
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Re: Number of square tiles needed to cover a space on a wall of 72 x 108 [#permalink] New post   16 Sep 2022, 07:07
Trying to figure out what I did wrong here. I got B .

A: length of one tile = perim / 4 = 9. tiles to cover width side =72/9 = 8 tiles to cover length side = 108/9 = 12. Whole area = 8*12 = 96
B: length of one tile = sqrt(area) = 3. tiles to cover width side =72/3 = 24 tiles to cover length side= 36. two sides each for rectangular border = 24*2 + 36*2 = 120
-- we already know B is greater, but to actually cover the whole border, we would need to cover the four corners with tiles too, bringing the total of B to 124.

did i misunderstand part of the question? Thanks
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Re: Number of square tiles needed to cover a space on a wall of 72 x 108 [#permalink] New post   16 Sep 2022, 07:20
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OE


Quote:
Explanation: Read carefully – did you notice that the tiles specified in Column A had a perimeter of 36 inches, while the tiles in Column B were specified using their area? This is especially easy to miss since 36 is a perfect square. For Column A, the tiles have side length of 36/4 = 9”. You will need 72/9 = 8 tiles along the width, and 108/9 = 12 tiles along the length; (12)(8) = 96 tiles. Now, since the square border tiles have area of 9 square inches, they must have side length of 3”. The width can be bordered by 72/3 = 24 tiles, while the length can be bordered by 108/3 = 36 tiles. Don’t forget there are two lengths and two widths, for a total of 24 + 24 + 36 + 36 = 120 tiles. (You might also want to add another 4 tiles, for the corners, but it doesn’t make a difference for this problem.)

So more 3” small tiles are needed for the border (120) than large 9” tiles for the area (96). If you had used 6” tiles for the area as the problem attempted to mislead you, you would have needed 216 of them and mistakenly chosen A.
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Re: Number of square tiles needed to cover a space on a wall of 72 x 108 [#permalink] New post   16 Sep 2022, 07:43
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Carcass wrote:
OE


Quote:
Explanation: Read carefully – did you notice that the tiles specified in Column A had a perimeter of 36 inches, while the tiles in Column B were specified using their area? This is especially easy to miss since 36 is a perfect square. For Column A, the tiles have side length of 36/4 = 9”. You will need 72/9 = 8 tiles along the width, and 108/9 = 12 tiles along the length; (12)(8) = 96 tiles. Now, since the square border tiles have area of 9 square inches, they must have side length of 3”. The width can be bordered by 72/3 = 24 tiles, while the length can be bordered by 108/3 = 36 tiles. Don’t forget there are two lengths and two widths, for a total of 24 + 24 + 36 + 36 = 120 tiles. (You might also want to add another 4 tiles, for the corners, but it doesn’t make a difference for this problem.)

So more 3” small tiles are needed for the border (120) than large 9” tiles for the area (96). If you had used 6” tiles for the area as the problem attempted to mislead you, you would have needed 216 of them and mistakenly chosen A.


Thanks for posting this, but does this mean the answer should be B (the Show Answer link above shows A)? Thx
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Re: Number of square tiles needed to cover a space on a wall of 72 x 108 [#permalink] New post   16 Sep 2022, 07:58
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pster79 wrote:
Carcass wrote:
OE


Quote:
Explanation: Read carefully – did you notice that the tiles specified in Column A had a perimeter of 36 inches, while the tiles in Column B were specified using their area? This is especially easy to miss since 36 is a perfect square. For Column A, the tiles have side length of 36/4 = 9”. You will need 72/9 = 8 tiles along the width, and 108/9 = 12 tiles along the length; (12)(8) = 96 tiles. Now, since the square border tiles have area of 9 square inches, they must have side length of 3”. The width can be bordered by 72/3 = 24 tiles, while the length can be bordered by 108/3 = 36 tiles. Don’t forget there are two lengths and two widths, for a total of 24 + 24 + 36 + 36 = 120 tiles. (You might also want to add another 4 tiles, for the corners, but it doesn’t make a difference for this problem.)

So more 3” small tiles are needed for the border (120) than large 9” tiles for the area (96). If you had used 6” tiles for the area as the problem attempted to mislead you, you would have needed 216 of them and mistakenly chosen A.


Thanks for posting this, but does this mean the answer should be B (the Show Answer link above shows A)? Thx


:(

The answer is indeed B but the book reports A in the OA. The explanation B
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Re: Number of square tiles needed to cover a space on a wall of 72 x 108 [#permalink]
16 Sep 2022, 07:58
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