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The figure above represents a square garden that is divided

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The figure above represents a square garden that is divided  [#permalink]

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Updated on: 06 Mar 2014, 02:13
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Difficulty:

55% (hard)

Question Stats:

73% (03:14) correct 27% (02:59) wrong based on 264 sessions

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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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Originally posted by mehdiov on 06 Sep 2010, 15:14.
Last edited by Bunuel on 06 Mar 2014, 02:13, edited 2 times in total.
Renamed the topic, edited the question and the OA.
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Re: The figure above represents a square garden that is divided  [#permalink]

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09 Sep 2016, 14:06
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Top Contributor
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mehdiov wrote:

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.

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 = 3/2

Cheers,
Brent
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Re: an other problem for this night  [#permalink]

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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 (OA must be wrong).
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Re: an other problem for this night  [#permalink]

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06 Sep 2010, 15:43
mehdiov wrote:
my answer is 1.5 but the OA is 2

You are continuously posting wrong OA's. Kindly check your source of Gmat tests.

The OA's on Gmat paper set can not be wrong, either you are following wrong source of sets or you are referring different answers from different sets.
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Re: an other problem for this night  [#permalink]

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06 Sep 2010, 15:48
gurpreetsingh wrote:
mehdiov wrote:
my answer is 1.5 but the OA is 2

You are continuously posting wrong OA's. Kindly check your source of Gmat tests.

The OA's on Gmat paper set can not be wrong, either you are following wrong source of sets or you are referring different answers from different sets.

Seorry about that ... I'm posting those questions because I'm surprised with the OA. the source of those question is paper test but the answers are provided from an organism "specialized" in GMAT courses ... Sorry again
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Re: an other problem for this night  [#permalink]

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06 Sep 2010, 15:51
You are welcome to post any question in which you have doubt. I was just concerned because I thought you might be following wrong source and it might bother you in your preparation. I think those answers are wrong, or those answers are referring wrong set of the sets.

Good luck.
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Re: The figure above represents a square garden that is divided  [#permalink]

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06 Mar 2014, 02:36
Bumping for review and further discussion.

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Re: The figure above represents a square garden that is divided  [#permalink]

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06 Mar 2014, 20:59
1
Refer figure below:

$$(6-x). 3 . 2 + 9 + 3x = \frac{81}{2}$$ (Area of shaded region = Area of non-shaded region; so dividing by 2)

Solving, we get x = 1.5 = Answer = C
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Re: The figure above represents a square garden that is divided  [#permalink]

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08 May 2014, 09:59
Just throwin' this one out

So we have that the area of the peas (shaded) equal to the areas of the other stuff

So basically 9+9+6x+3y=9+3y+3y+3x

So y-x = 3

Now, we also know that y+x = 3 from the fact the the garden is a square.

Therefore x = 1.5

Holla at me if you have any doubts
Cheers

J
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Re: The figure above represents a square garden that is divided  [#permalink]

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04 Jun 2018, 09:50
Sorry for digging this one out, GMATPrepNow

Where is the "6-x" stemming from?

Thanks!
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Re: The figure above represents a square garden that is divided  [#permalink]

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04 Jun 2018, 10:01
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Top Contributor
Sorry for digging this one out, GMATPrepNow

Where is the "6-x" stemming from?

Thanks!

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
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Re: The figure above represents a square garden that is divided  [#permalink]

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04 Jun 2018, 10:05
It does!

Thank you!
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Re: The figure above represents a square garden that is divided  [#permalink]

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30 Sep 2019, 11:06
mehdiov wrote:

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

You can use backsolving and a bit of logic to figure this one quickly:
We know that the garden is a square, with sides that are 9.
That means the Area of the Square is 81 meters squared.

We also know that the shaded region of peas is equal to unshaded regions of tomatoes;
So the area for each (peas and tomatoes) is 81/2 = 40.5
Off the bat we know that B and D can't be the answer (it has to be a non-integer number), BUT we can use B and D as test values as they're easier to work with.

B: 1
The shaded area the 2 boxes on the left side is 3 meters squared each (3*1) and the shaded area for the middlebox would be 15 (3*5).
The area of all of the shaded boxes would be (9+9+15+3+3) = 39, which is less than 40.5. That means A and B are out, so we need to test a bigger number.

D:2
The shaded area of the 2 boxes on the left side is 6 meters squared each (3*2) and the shaded area for the middlebox would be 12 (3*4).
The area of all of the shaded boxes would be (9+9+12+6+6) = 42, which is larger than 40.5. That means C has to be the answer!

Re: The figure above represents a square garden that is divided   [#permalink] 30 Sep 2019, 11:06
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