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605-655 (Medium)|   Geometry|      
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GMATBusters
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A square with a side of 5 is positioned with its Corner in the center 05 Oct 2018, 22:42
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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45% (medium)

Question Stats:

71% (02:40) correct 29% (02:30) wrong based on 72 sessions

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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


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C
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warrior1991
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A square with a side of 5 is positioned with its Corner in the center 05 Oct 2018, 23:10
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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.
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A square with a side of 5 is positioned with its Corner in the center 05 Oct 2018, 23:12
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OA = C, provide your explanation

warrior1991
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.
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warrior1991
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A square with a side of 5 is positioned with its Corner in the center 05 Oct 2018, 23:40
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Please let me know if there is any easy way for solving this question.
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warrior1991
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A square with a side of 5 is positioned with its Corner in the center 05 Oct 2018, 23:42
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Bunuel

Sir what are your thoughts on this?? How should we approach to this question??
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warrior1991
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A square with a side of 5 is positioned with its Corner in the center 05 Oct 2018, 23:43
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gmatbusters
OA = C, provide your explanation

warrior1991
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.
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By the way, what is the source of this question??
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Mike03
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A square with a side of 5 is positioned with its Corner in the center 06 Oct 2018, 00:08
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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/
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warrior1991
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A square with a side of 5 is positioned with its Corner in the center 06 Oct 2018, 00:16
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Mike03
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/
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Thanks for sharing !! Completely surprised by this!! It was so easy after seeing the video in your link !!!
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A square with a side of 5 is positioned with its Corner in the center 06 Oct 2018, 00:32
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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
WhatsApp Image 2018-10-06 at 13.07.37.jpeg [ 55.96 KiB | Viewed 6242 times ]
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A square with a side of 5 is positioned with its Corner in the center 06 Oct 2018, 09:03
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gmatbusters

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


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I followed this approach -
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WhatsApp Image 2018-10-06 at 9.31.35 PM.jpeg
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A square with a side of 5 is positioned with its Corner in the center 06 Oct 2018, 21:50
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C) Very nice


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ananya1322
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A square with a side of 5 is positioned with its Corner in the center 02 Aug 2025, 03:42
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How did we get the length of AP in the diagram? I am unable to understand
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Bunuel
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A square with a side of 5 is positioned with its Corner in the center 02 Aug 2025, 08:36
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ananya1322
How did we get the length of AP in the diagram? I am unable to understand
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This is a geometry question, which is not part of the GMAT Focus Edition, so you can skip it and move on.
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Aurellius
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A square with a side of 5 is positioned with its Corner in the center 04 Aug 2025, 07:07
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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
warrior1991
Please let me know if there is any easy way for solving this question.
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A square with a side of 5 is positioned with its Corner in the center 04 Aug 2025, 07:10
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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
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