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GMAT Set 5 Q8

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by Uva@90 » Wed Feb 18, 2015 4:06 am
Abhijit K wrote:Please help me solve Q8 in the attachment.

Thanks in advance.

Hi Abhijit,

Is OA [spoiler]C= 1.5[/spoiler]

Regards,
Uva.
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by GMATGuruNY » Wed Feb 18, 2015 7:26 am
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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
Since the right side of the of the garden = 3+3+3 = 9, the area of the garden = 9*9 = 81.
Since the unshaded area and the shaded area are equal, the total area of the unshaded regions = 81/2 = 40.5.
We can PLUG IN THE ANSWERS, which represent the value of x.
When the correct answer choice is plugged in, unshaded area = 40.5.

Answer choice D: x=2
Image
Unshaded area = 6+12+9+12 = 39.
Too small.
Eliminate D.

Answer choice B: x=1
Image
Unshaded area = 3+15+9+15 = 42.
Too big.
Eliminate B.

Since D yields a result that is TOO SMALL, while B yields a result that is TOO BIG, the correct answer choice must be BETWEEN B AND D.

The correct answer is C.

Note:
Some versions of this problem incorrectly indicate that the OA is D.
As shown below, the OA is not D but C.

Answer choice C: x=1.5
Image
Unshaded area = 4.5 + 13.5 + 9 + 13.5 = 40.5
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by Brent@GMATPrepNow » Wed Feb 18, 2015 8:44 am
Image

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
First recognize that the middle length must be 6-x.
Then we can find the areas of all 9 rectangles.
Image

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.

3x + 3x + 3(6-x) + 9 + 9 = 3x + 3(6-x) + 3(6-x) + 9
3x + 36 = -3x + 45
6x = 9
x = 9/6 = [spoiler]3/2 = C[/spoiler]

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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