set6 Q8 - PS

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set6 Q8 - PS

by arocks » Thu Oct 04, 2007 2:31 am
Please explain!!

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

Thanks.
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Re: set6 Q8 - PS

by ratindasgupta » Thu Oct 04, 2007 4:45 am
arocks wrote:Please explain!!

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

Thanks.
Assume that the middle portion has length a.

So total area can be equated as

81 = 27 + 9a + 9x
a + x = 6

Also since the sums of the shaded areas and white areas are the same, they too can be equated by

18 + 3a + 6x = 9 + 6a + 3x
a - x = 3

a = 4.5. So x = 1.5

Answer is C

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by arocks » Thu Oct 04, 2007 5:49 am
Thanks this makes perfect sense. The OA is D, which is incorrect i believe.