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A rectangular tiled floor consists of 70 square tiles. The rectangular

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Bunuel
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A rectangular tiled floor consists of 70 square tiles. The rectangular [#permalink] New post   13 Jun 2019, 00:13
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A rectangular tiled floor consists of 70 square tiles. The rectangular floor is being rearranged so that 2 tiles will be removed from each row of tiles and 4 more rows of tiles will be added. After the change in layout, the floor will still have 70 tiles, and it will still be a rectangle. How many rows were in the tile floor before the change in layout?

A. 4
B. 7
C. 10
D. 14
E. 28
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C
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Re: A rectangular tiled floor consists of 70 square tiles. The rectangular [#permalink] New post   13 Jun 2019, 02:44
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Bunuel wrote:
A rectangular tiled floor consists of 70 square tiles. The rectangular floor is being rearranged so that 2 tiles will be removed from each row of tiles and 4 more rows of tiles will be added. After the change in layout, the floor will still have 70 tiles, and it will still be a rectangle. How many rows were in the tile floor before the change in layout?

A. 4
B. 7
C. 10
D. 14
E. 28


test with given options
(10+4)*(7-2) = 14*5 = 70
IMO C
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Re: A rectangular tiled floor consists of 70 square tiles. The rectangular [#permalink] New post   13 Jun 2019, 02:59
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Let number of rows = n, and number of tiles in each row= x

Given that- nx=70 and (n+4)(x-2)=70

(n+4)(x-2)=70
nx+4x-2n-8=70
70+4x-2n-8=70
2x-n=4
\(\frac{140}{n} - n = 4\)
n=10 and x=7



Bunuel wrote:
A rectangular tiled floor consists of 70 square tiles. The rectangular floor is being rearranged so that 2 tiles will be removed from each row of tiles and 4 more rows of tiles will be added. After the change in layout, the floor will still have 70 tiles, and it will still be a rectangle. How many rows were in the tile floor before the change in layout?

A. 4
B. 7
C. 10
D. 14
E. 28
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Re: A rectangular tiled floor consists of 70 square tiles. The rectangular [#permalink] New post   13 Jun 2019, 08:20
Bunuel wrote:
A rectangular tiled floor consists of 70 square tiles. The rectangular floor is being rearranged so that 2 tiles will be removed from each row of tiles and 4 more rows of tiles will be added. After the change in layout, the floor will still have 70 tiles, and it will still be a rectangle. How many rows were in the tile floor before the change in layout?

A. 4
B. 7
C. 10
D. 14
E. 28


The various rectangles that can be formed are 70*1, 35*2, 10*7, and 14*5.

If we remove 2 tiles from each row, the rectangles 70*1 and 35*2 will not remain rectangular

Lets consider 10 rows of 7 tiles each. If we remove 2 tiles each, we will be left with 14 rows of
5 tiles each which will be shaped like a rectangle.

Therefore, there were 10 rows(Option C) in the tile floor before the change in layout happened.
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Re: A rectangular tiled floor consists of 70 square tiles. The rectangular [#permalink] New post   28 Apr 2020, 14:10
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Bunuel wrote:
A rectangular tiled floor consists of 70 square tiles. The rectangular floor is being rearranged so that 2 tiles will be removed from each row of tiles and 4 more rows of tiles will be added. After the change in layout, the floor will still have 70 tiles, and it will still be a rectangle. How many rows were in the tile floor before the change in layout?

A. 4
B. 7
C. 10
D. 14
E. 28


Hi Bunuel
Can you help me with the solution.
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Re: A rectangular tiled floor consists of 70 square tiles. The rectangular [#permalink]
28 Apr 2020, 14:10
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