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
The OA is the option C.
I got confused. <i class="em em-confused"></i> Could someone give me some help, please? Thanks in advance.
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A rectangular tiled patio is composed of 70 square tiles.
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Let R = the number of rows and C = the number of columns.M7MBA wrote: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
Total number of tiles = RC.
Since there are 70 tiles, we get:
70 = RC.
We can PLUG IN THE ANSWERS, which represent the value of R.
The equation in blue indicates that the value of R must be a FACTOR OF 70.
Of the five answer choices, only A and C divide evenly into 70.
Eliminate B, D and E.
After the layout changes so that there are 4 more rows and 2 fewer columns, the number of tiles remains 70.
Thus:
70 = (R+4)(C-2).
The equation in red indicates that R+4 must be factor of 70.
Option A implies that R+4 = 5+4 = 9, which is NOT a factor of 70.
Eliminate A.
The correct answer is C.
C: 10 rows
Current arrangement:
70 = 10C
C = 7.
After the layout changes, there are 4 more rows (for a total of 14 rows) and 2 fewer columns (for a total of 5 columns);
70 = 14*5.
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This problem is about the factors of 70:M7MBA wrote: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
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
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Hi M7MBA,
We're told that 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 and after the change in layout, the patio will still have 70 tiles, and it will still be rectangular. We're asked for the number of rows that were in the tile patio BEFORE the change in layout. This question comes down to some basic Arithmetic and the willingness to 'play around' with the prompt a bit.
To start, since we have a rectangle comprised of 70 square times, the number of rows all have the SAME number of tiles and the number of columns have the SAME number of times. This means that we're looking for 2 integers that multiply together to get 70. After making the changes to the number of columns and the number of rows, we STILL end up with 70 square tiles, but we'll be dealing with two different numbers for length and width. Since those changes are relatively small, it's likely that we're dealing with two starting numbers that are relatively close together. The most obvious pair would be 7 and 10.
(7 columns )(10 rows) = 70 tiles
Reducing the number of columns by 2 and increasing the number of rows by 4 gives us....
(4 columns )(14 rows) = 70 tiles
This matches what we were told, so this MUST be the answer. The beginning number of ROWS is 10.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
We're told that 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 and after the change in layout, the patio will still have 70 tiles, and it will still be rectangular. We're asked for the number of rows that were in the tile patio BEFORE the change in layout. This question comes down to some basic Arithmetic and the willingness to 'play around' with the prompt a bit.
To start, since we have a rectangle comprised of 70 square times, the number of rows all have the SAME number of tiles and the number of columns have the SAME number of times. This means that we're looking for 2 integers that multiply together to get 70. After making the changes to the number of columns and the number of rows, we STILL end up with 70 square tiles, but we'll be dealing with two different numbers for length and width. Since those changes are relatively small, it's likely that we're dealing with two starting numbers that are relatively close together. The most obvious pair would be 7 and 10.
(7 columns )(10 rows) = 70 tiles
Reducing the number of columns by 2 and increasing the number of rows by 4 gives us....
(4 columns )(14 rows) = 70 tiles
This matches what we were told, so this MUST be the answer. The beginning number of ROWS is 10.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
