In the figure above, a rectangle is divided into smaller rectangles

Question

https://gmatclub.com/forum/download/file.php?id=39905 In the figure above, a rectangle is divided into smaller rectangles of the same shape and size. What is the area of the large rectangle? (1) The length of the darkened path at the top of the diagram is 45. (2) The length of the darkened path at the bottom of the diagram is 39. 2018-02-08_1724.png

mygmat0101 · Answer

Answer is D

Each statement alone is enough to answer
You need to observe carefully to answer this question
consider the length n breadth to be "l" , "b"
 
1) the total length is 3l+3b
 we can find value of l+b and the perimeter of big rectangle too
 2)the total length is 3l+3b
 we can find value of l+b and the perimeter of big rectangle too

almazovniko · Answer

Very cool question.

Here is how I solved it:

Statement 1

The length of the top path is 45. When I look at the top side and the bottom side, since its a rectangle, they should be equal. Bottom side has 2 long sides, top side has 1 long side and 3 short sides. Therefore, 1 long side = 3 short sides.

The top path consists of 3 long sides and 3 short sides. We know that 3 short sides = 1 long side. Therefore 4 long sides = 45. No need to go further. This is enough to find out the area of the large triangle.

Sufficient

Statement 2

Same as above, but 39 in length and it has 4 short sides and 3 long sides. Logic above can apply for this. No need to calculate anything.

Sufficient

Kudos if helped.

PierTotti17 · Answer

Got answer D, but I think it would not appear on GMAT since each statement yields a different area.

Statement 1 --> 12x=45 --> x=45/12 or x= 15/4

Height (big rectangle) = 7x
Length = 6x
Area = 6x*7x = 590.625

Sufficient.

Statement 2 --> 13x = 39 --> x=3
Area =7(3)*6(3) = 378

2 different answers. But nonetheless, the area can be found using either statement.

kylebecker9 · Answer

We can see that 3 short sides = 1 long side.

Each statement gives us a second question that allows us to solve for both variables. Thus, each is sufficient.

The problem is a bit confusing to me since each statement creates a different answer to the overall question, and I would not expect the statements to conflict with one another. Am I wrong about this conflict?

Pranjal3107 · Answer

Hi Can anyone explain the long side and short side ? Is it the length and breadth we're talking about here ?
Sorry for such a silly question.

Basshead · Answer

Each smaller rectangle = length : width = 3 : 1

Each path represents a number of lengths and widths. If we're given the length of either path, we can then determine the perimeter of the larger rectangle.

Therefore each statement alone is sufficient.

Basshead · Answer

I think GMAC realized the two statements above contradict each other; on the current question in GMAT Prep the diagram and statements are different:

________________

As shown above, a rectangle is divided into smaller rectangles of the same size and shape. What is the perimeter of the large rectangle?

(1) The length of the darkened path on the right is 36.
(2) The length of the darkened path on the left is 54.

Bunuel  do you mind updating?

Bunuel · Answer

You are right. This is not a GMAT Prep question. This one is from Pearson. I posted GMAT Prep question here: https://gmatclub.com/forum/as-shown-abo ... 40512.html Thank you!

In the figure above, a rectangle is divided into smaller rectangles

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