Q. A rectangular lawn of length 200m by 120m has two roads running along its center, one along the length and the other along the width. If the width of the roads is 5m what is the area covered by the two roads?
A. 1600
B. 400
C. 1625
D. 1575
E. 1550
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Hi Joy Shaha,
This question is a bit oddly worded, but the 'intent' is to see whether you 'double-count' the overlapping space or not (the part that is covered by BOTH the roads in the 'corner' of the rectangle).
To start, we have a rectangle that is 200m x 120m. There's a 5m wide road that runs the entire length of the rectangle and one that runs the entire width of the rectangle. The areas of the individual roads are...
(5m)(200m) = 1000 m^2
(5m)(120m) = 600 m^2
However, these two roads 'overlap', creating a (5m)(5m) = 25 m^2 space in the corner in which they meet. That space is included in BOTH of those calculations though, so we have to remove one iteration of it. This leaves us with a total 'road area' of...
1000 + 600 - 25 = 1575 m^2
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
This question is a bit oddly worded, but the 'intent' is to see whether you 'double-count' the overlapping space or not (the part that is covered by BOTH the roads in the 'corner' of the rectangle).
To start, we have a rectangle that is 200m x 120m. There's a 5m wide road that runs the entire length of the rectangle and one that runs the entire width of the rectangle. The areas of the individual roads are...
(5m)(200m) = 1000 m^2
(5m)(120m) = 600 m^2
However, these two roads 'overlap', creating a (5m)(5m) = 25 m^2 space in the corner in which they meet. That space is included in BOTH of those calculations though, so we have to remove one iteration of it. This leaves us with a total 'road area' of...
1000 + 600 - 25 = 1575 m^2
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
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Jay@ManhattanReview
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Hi Joy,Joy Shaha wrote:Q. A rectangular lawn of length 200m by 120m has two roads running along its center, one along the length and the other along the width. If the width of the roads is 5m what is the area covered by the two roads?
A. 1600
B. 400
C. 1625
D. 1575
E. 1550
So this is lawn is of the shape of England's flag.
The area covered by the two roads = 5 * (Length of the lawn + Width of the lawn) - Common square intersecting area of the roads*
*counted twice
=> The area covered by the two roads = 5 * (200 + 120) - 5 * 5 = 1600 - 25 = 1575 m^2
OA: D
-Jay
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