A square with a side of 5 is positioned with its Corner in the center

Question

https://gmatclub.com/forum/download/file.php?id=44196 A square with a side of 5 is positioned with its Corner in the center of a square with a side of 4, as shown. One side of the overlapping region is equal to 3. What is the area Of overlap between the two squares (the area of the red shape)? (A) \frac{3}{(\sqrt{2})} (B) 2 (C) 4 (D) \frac{6}{(\sqrt{3})} (E) 5 GC.jpg

warrior1991 · Answer

IMO C.
I did not use the big square in my calculation.If you divide the square with side 4 into halves vertically as well as horizontally each side of the 4 smaller square formed will be 2. From there we can proceed further.

Let me know if my answer is correct. I will share the diagrammatic representation of my solution.

GMATBusters · Answer

OA = C, provide your explanation

warrior1991 · Answer

Please let me know if there is any easy way for solving this question.

warrior1991 · Answer

Bunuel

Sir what are your thoughts on this?? How should we approach to this question??

warrior1991 · Answer

By the way, what is the source of this question??

Mike03 · Answer

A very good question. Although I was not able to solve this after spending ~20 min I found the solutions online. Posting the link below: https://mindyourdecisions.com/blog/2018 ... es-riddle/

warrior1991 · Answer

Thanks for sharing !! Completely surprised by this!! It was so easy after seeing the video in your link !!!

GMATBusters · Answer

Visualization approach

The corner of the 5-square is aligned to the centre of the 4-square. If the overlap was at 90deg then the area would have been exact 1/4( See figure)

Even if we rotate the 5-square at an angle (like in the image), still hinges at the centre, the overlap area should remain the same.

Hence overlap = Area of small square /4 = 16/4 = 4

Attachment:

WhatsApp Image 2018-10-06 at 13.07.37.jpeg [ 55.96 KiB | Viewed 6362 times ]

rahul16singh28 · Answer

I followed this approach -

Ahmadd · Answer

C) Very nice

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ananya1322 · Answer

How did we get the length of AP in the diagram? I am unable to understand

Bunuel · Answer

This is a geometry question, which is  not part of the GMAT Focus Edition , so you can skip it and move on.

Aurellius · Answer

how did you get the value of 1 in that triangle because it could be 0.7 as well we dont really have an info like that

Aurellius · Answer

im getting a C as well. 
im assuming that we can draw a trapezium and first find the area of that then we can make a smaller triangle with base 1 and height 2. then we can subtract the area of that trapezium from that triangle to get the result as 4

A square with a side of 5 is positioned with its Corner in the center

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A square with a side of 5 is positioned with its Corner in the center

Prep Toolkit

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