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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
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A rectangular tiled patio is composed of 70 square tiles. The rectangu...
Given:
- The rectangular tiled patio is composed of 70 square tiles.
- After rearrangement, there will be 2 fewer columns of tiles and 4 more rows of tiles.
- The patio will still have 70 tiles after the rearrangement.
- The patio will still be rectangular.
To find:
The number of rows in the tile patio before the change in layout.
Solution:
Let's assume the original number of columns in the patio is 'c' and the original number of rows is 'r'.
Step 1: Determine the number of tiles in the original patio
- The number of tiles in the original patio is given as 70 square tiles.
Step 2: Set up an equation using the given information
- The number of tiles in the original patio is equal to the number of tiles in the rearranged patio.
- Since the number of tiles in the rearranged patio is also 70, we can write the equation as:
c * r = (c - 2) * (r + 4)
Step 3: Simplify the equation
- Expand the right side of the equation:
c * r = c * r + 4c - 2r - 8
- Simplify:
4c - 2r - 8 = 0
Step 4: Solve the equation
- Rearrange the equation to isolate 'r':
2r = 4c - 8
r = (4c - 8) / 2
r = 2c - 4
Step 5: Test different values of 'c' to find the number of rows 'r'
- Since 'c' and 'r' must be positive integers, we can test different values of 'c' to find a valid value for 'r' which gives the original number of tiles.
- Let's test 'c' = 5:
r = 2(5) - 4
r = 6
- Testing other values of 'c' would not yield a valid value for 'r'.
Step 6: Conclusion
- The number of rows in the tile patio before the change in layout is 6.
- Therefore, the correct answer is option 'b) 6'.
- The rectangular tiled patio is composed of 70 square tiles.
- After rearrangement, there will be 2 fewer columns of tiles and 4 more rows of tiles.
- The patio will still have 70 tiles after the rearrangement.
- The patio will still be rectangular.
To find:
The number of rows in the tile patio before the change in layout.
Solution:
Let's assume the original number of columns in the patio is 'c' and the original number of rows is 'r'.
Step 1: Determine the number of tiles in the original patio
- The number of tiles in the original patio is given as 70 square tiles.
Step 2: Set up an equation using the given information
- The number of tiles in the original patio is equal to the number of tiles in the rearranged patio.
- Since the number of tiles in the rearranged patio is also 70, we can write the equation as:
c * r = (c - 2) * (r + 4)
Step 3: Simplify the equation
- Expand the right side of the equation:
c * r = c * r + 4c - 2r - 8
- Simplify:
4c - 2r - 8 = 0
Step 4: Solve the equation
- Rearrange the equation to isolate 'r':
2r = 4c - 8
r = (4c - 8) / 2
r = 2c - 4
Step 5: Test different values of 'c' to find the number of rows 'r'
- Since 'c' and 'r' must be positive integers, we can test different values of 'c' to find a valid value for 'r' which gives the original number of tiles.
- Let's test 'c' = 5:
r = 2(5) - 4
r = 6
- Testing other values of 'c' would not yield a valid value for 'r'.
Step 6: Conclusion
- The number of rows in the tile patio before the change in layout is 6.
- Therefore, the correct answer is option 'b) 6'.
Community Answer
A rectangular tiled patio is composed of 70 square tiles. The rectangu...
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
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
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
2r2 - 4r - 70=0
r2 - 2r - 35 = 0
r2 -7r +5r - 35 = 0
r = -5,7
r cannot be negative so r = 7
and c = 10
So, Answer will be C
c*r = (r - 2)*(c + 4)
=> 4r -2c = 8
c = 2r - 4
Putting it in c * r = 70
(2r - 4) * r = 70
2r2 - 4r - 70=0
r2 - 2r - 35 = 0
r2 -7r +5r - 35 = 0
r = -5,7
r cannot be negative so r = 7
and c = 10
So, Answer will be C
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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)5b)6c)10d)13e)28Correct answer is option 'C'. Can you explain this answer?
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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)5b)6c)10d)13e)28Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about 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)5b)6c)10d)13e)28Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)5b)6c)10d)13e)28Correct answer is option 'C'. Can you explain this answer?.
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)5b)6c)10d)13e)28Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about 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)5b)6c)10d)13e)28Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)5b)6c)10d)13e)28Correct answer is option 'C'. Can you explain this answer?.
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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)5b)6c)10d)13e)28Correct answer is option 'C'. Can you explain this answer?, a detailed solution for 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)5b)6c)10d)13e)28Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of 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)5b)6c)10d)13e)28Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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