The figure above represents a square garden that is divided

Question

https://gmatclub.com/forum/download/file.php?id=66541 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 Document1.doc 2022-05-07_17-47-08.png

BrentGMATPrepNow · Accepted Answer

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) 
 https://i.imgur.com/kK1C5pX.png

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

Bunuel · Answer

https://gmatclub.com/forum/download/file.php?id=66541

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

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.

BigAdam · Answer

Sorry for digging this one out,  GMATPrepNow

Where is the "6-x" stemming from?

Thanks!

BrentGMATPrepNow · Answer

Notice the dimensions at the very bottom of the diagram (showing the width of the large square).
We have  x, blank, and 3

Now notice that the larger square has a height of  9  (3 + 3 + 3 =  9 )

Since we're told that the entire garden is SQUARE, we know that the  width  = the  height

In other words,  x + ? + 3  =  9 
Subtract 3 from both sides to get: x + ? = 6
Subtract x from both sides to get: ? =   6 - x

Does that help?

Cheers,
Brent

sing086 · Answer

This question is a major speed breaker and has a high chance of making a mistake, took me 4 mins to solve (got areas of few boxes wrong the first time). Any alternate approach to the ones mentioned on this thread ?

Bunuel GMATNinja

Bunuel   GMATNinja

GMATNinja · Answer

For an elegant and efficient approach to this question, check out  this explanation  by  PareshGmat . I'm not sure that it's possible to improve on that solution for this particular question.

For whatever it's worth, if you saw this question on an actual exam and couldn't find an efficient solution path, it definitely wouldn't be worth fighting with the question for four minutes. Sometimes, the GMAT is all about picking your battles, especially on quant. For more on GMAT time management, check out  this video .

I hope that helps a bit!

Kimberly77 · Answer

Great visual explanation  BrentGMATPrepNow , however not quite sure on the same shaded region that one side is 3x but the other side is 9? Could you help explain? Thanks

BrentGMATPrepNow · Answer

I'm not sure what you're asking. 
Can you please rephrase your question?

I should note is that the numbers  inside  each box represent the area of that box (not the dimensions of the box)

Kimberly77 · Answer

Thanks  BrentGMATPrepNow  for your quick reply. How did you derive numbers 9 inside those 3 boxes ? as the first 3 are 3 which make sense. Thanks

BrentGMATPrepNow · Answer

Each individual box in the left hand column has width = x and height equal 3. 
So, the area of each box in the left-hand column = (base)(height) = (x)(3) = 3x

Also notice that the middle column has width 6 - x
Also, each box in the middle column has height 3
So, the area of each box in the left-hand column = (base)(height) = (6 - x)(3) = 18 - 3x

Does that help?

JYnaey · Answer

This is how I solved the question.

1) Among the 3 rows,
 Black vs. White areas of above "two" rows are always the same, 
 whatever the length of X.

2) So I just calculate bottom row, especially just length only. 
 I don't try to calculate area and as height is all the same = 3.

3) equation: x + 3 (black) = 6 - x (white)

x = 1.5 (answer : C)

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The figure above represents a square garden that is divided

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