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C
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Difficulty:
45%
(medium)
Question Stats:
75% (03:09) correct
25%
(03:06)
wrong
based on 1334
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The figure above represents a square garden that is divided into 9 rectangular regions with indicated dimensions in meters. The shaded regions are planted with peas, and the unshaded regions are planted with tomatoes. If the sum of the areas of the regions planted with peas is equal to the sum of the areas of the regions planted with tomatoes, what is the value of x?
A. 0.5
B. 1
C. 1.5
D. 2
E. 2.5
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Attachment:
2022-05-07_17-47-08.png [ 8.48 KiB | Viewed 20237 times ]
Updated on: 16 Feb 2021, 13:08
Originally posted by BrentGMATPrepNow on 09 Sep 2016, 14:06.
Last edited by BrentGMATPrepNow on 16 Feb 2021, 13:08, edited 2 times in total.
Last edited by BrentGMATPrepNow on 16 Feb 2021, 13:08, edited 2 times in total.
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mehdiov
The three given lengths on the right sides of the diagram add to 9
Since we're told the garden is a SQUARE, we know that the 3 lengths on the bottom of the diagram must add to 9.
In other words: x + (missing middle length) + 3 = 9
Solve to get: middle length must be 6-x.
At this point, we can find the areas of all 9 rectangles by applying the formula area of rectangle = (base)(height)
The sum of the areas of the regions planted with peas is equal to the sum of the areas of the regions planted with tomatoes.
We can write: 3x + 3x + 3(6-x) + 9 + 9 = 3x + 3(6-x) + 3(6-x) + 9
Expand: 3x + 3x + 18 - 3x + 9 + 9 = 3x + 18 - 3x + 18 - 3x + 9
Simplify: 3x + 36 = -3x + 45
Add 3x to both sides: 6x + 36 = 45
Subtract 36 from both sides: 6x = 9
Solve: x = 9/6 = 3/2 = 1.5
Answer: C
Cheers,
Brent
06 Sep 2010, 15:30
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The figure above represents a square garden that is divided into 9 rectangular regions with indicated dimensions in meters. The shaded regions are planted with peas, and the unshaded regions are planted with tomatoes. If the sum of the areas of the regions planted with peas is equal to the sum of the areas of the regions planted with tomatoes, what is the value of x?
A. 0.5
B. 1
C. 1.5
D. 2
E. 2.5
As the garden is square then the base must also equal to 9, so the middle piece of base equals to \(9-3-x=6-x\).
As area of the shaded region equals to the area of unshaded region then:
\(18+6x+3*(6-x)=9+2*3(6-x)+3x\);
\(x=1.5\).
Answer: C.
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