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# The big outside purple square above has an area of 84

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Magoosh GMAT Instructor
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The big outside purple square above has an area of 84 [#permalink]

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13 May 2013, 10:53
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square with area 84.JPG [ 22.64 KiB | Viewed 1037 times ]

The big outside purple square above has an area of 84, and the dots are all equal spaced, forming smaller squares. What is the sum of the areas of the shaded yellow regions?
(A) 20
(B) 24
(C) 28
(D) 32
(E) 36

GMAT students often say, "I could do better on the GMAT Quant if I had unlimited time, but I am always running of time on the hard problems, and I don't know how to do the math faster." Problems such as this, when done via a methodical, long, tedious calculation, can take quite some time, and open up the possibility of numerous calculation errors. When a problem like this appears on the GMAT, there simply has to be some insight method that presents a shortcut to the answer, much easier than the long tedious piece-by-piece calculation.

See this blog for a detailed discussion of this problem-solving perspective:
http://magoosh.com/gmat/2013/how-to-do- ... th-faster/
as well as a complete solution to this particular question.

Experts: any tips you would like to add for doing GMAT math faster?

Mike
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Re: The big outside purple square above has an area of 84 [#permalink]

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13 May 2013, 11:02
there are 7X7 squares. Area of each square is 84/49.

Now count the no of squares in yellow. If you face a triangle, try analysing it as a half of rectangle (2square). The total no of squares will be 24.
24 * 84/49 = 24.
IMO B.

Took me 01:59.

Any simpler approach?
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Re: The big outside purple square above has an area of 84 [#permalink]

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13 May 2013, 11:07
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We can solve this in 30 sec if we traspose the figures(refer to the image)

The area covered is $$\frac{2}{7}$$ of the total (2 columns)

So area is $$84*\frac{2}{7}=24$$
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square with area 84.JPG [ 33.21 KiB | Viewed 1016 times ]

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Re: The big outside purple square above has an area of 84 [#permalink]

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13 May 2013, 11:08
Did take lil time to figure out the trick to it! The answer is [B]

The trick is to place all the cut sections together and realize that they form a rectangle of 2x*x/ 7 are where x is the side. We already know that x^2 = 84. If we substitute the values we can find that the answer is 24! took me 1:58. I believe this is the shortest way to it

Regards,
Arpan
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Re: The big outside purple square above has an area of 84 [#permalink]

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13 May 2013, 12:03
arpanpatnaik wrote:
Did take lil time to figure out the trick to it! The answer is [B]

The trick is to place all the cut sections together and realize that they form a rectangle of 2x*x/ 7 are where x is the side. We already know that x^2 = 84. If we substitute the values we can find that the answer is 24! took me 1:58. I believe this is the shortest way to it

Regards,
Arpan

Yeah it might take 30+ seconds just to see the trick of moving the triangles over, it certainly wasn't obvious to me at first. But the shapes of the three figures hint at how the three shapes interconnect, in particular the one block on its own and the triangular shape missing only one square. Once you put them together the yellow portions fill 2 entire columns out of 7, and if you're familiar with the multiplication table you may quickly identify 84 as being 12 x 7, meaning that you have 2/7 of the table filled, with each 1/7 corresponding to exactly 12 units. Ergo, 24. Good question! It took me about a minute just to see the trick and then 15 seconds from there. Sometimes it's good to spend a little time figuring out the correct way instead of diving into calculating the area of irregular shapes.

Hope this helps!
-Ron
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Re: The big outside purple square above has an area of 84 [#permalink]

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13 May 2013, 12:04
This is easy - with a little experience at pattern recognition!

If you put the regions shaded in yellow together - you will be able to fill up two rows of squares - completely. The area of the shaded region, therefore is 2/7th of 84 or 24 units.

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Re: The big outside purple square above has an area of 84 [#permalink]

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19 Jan 2015, 06:46
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Re: The big outside purple square above has an area of 84   [#permalink] 19 Jan 2015, 06:46
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