A rectangular tiled patio is composed of 70 square tiles.

Question

A rectangular tiled patio is composed of 70 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 70 tiles, and it will still be rectangular. How many rows are in the tile patio before the change in layout?

A. 5
B. 6
C. 10
D. 13
E. 28

A. 5
B. 6
C. 10
D. 13
E. 28

ScottTargetTestPrep · Accepted Answer

This problem is about the factors of 70:

70 = 1 x 70 = 2 x 35 = 5 x 14 = 7 x 10

From the last two products of 70, we see that the original layout must be 7 columns and 10 rows so that the new layout will be 5 columns and 14 rows. So originally, there are 10 rows.

Answer: C

piyushksharma · Answer

Answer choices are:
A. 5
B. 6
C. 10
D. 13
E. 28

Bunuel · Answer

r*c=70 and (r+4)(c-2)=70 --> r=10 and c=7.

Answer: C.

PareshGmat · Answer

Say rows = x, then columns  = \frac{70}{x}

After change, rows = x+4, columns  = \frac{70}{x} - 2

Setting up the equation

(x+4)(\frac{70}{x} - 2) = 70

x^2 + 4x - 140 = 0

x = 10

Answer = C

BrushMyQuant · Answer

Suppose there are c columns and there are r rows
Original Situation
So, Number of tiles = c*r = 70
Also. Reach column has r tiles and each row has c tiles

New Situation
Number of tiles in each column is r-2 and number of tiles in each row is c+4
So, number of rows = r-2 and number of columns is c+4
So, Number of tiles = (r-2)*(c+4) = 70

Comparing both of them we get
c*r = (r-2)*(c+4)
=> 4r -2c = 8
c = 2r - 4

Putting it in c*r=70
(2r-4)*r = 70
2r^2 - 4r - 70=0
r^2 - 2r - 35 = 0
r^2 -7r +5r - 35 = 0
r = -5,7
r cannot be negative so r = 7
and c = 10

So, Answer will be C
hope it helps!

DeepikaBurre · Answer

A rectangular tiled floor is composed of 70 square tiles. The rectangular floor is rearranged so that 2 tiles are removed from each column and 4 tiles are added to each row. After the change in layout, the floor will still have 70 tiles, and still be rectangular. How many columns are in the tile floor before the change in layout?

A) 12

B) 7

C) 10

D) 14

E) 28

A) 12

B) 7

C) 10

D) 14

E) 28

Bunuel · Answer

Merging topics. Please refer to the discussion above. P.S. Also, please search before posting and name topics properly (check rule 3 here: rules-for-posting-please-read-this-before-posting-133935.html)

bumpbot · Answer

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A rectangular tiled patio is composed of 70 square tiles.

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A rectangular tiled patio is composed of 70 square tiles.

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