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

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Senior DS Moderator
Joined: 27 Oct 2017
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A square with a side of 5 is positioned with its Corner in the center  [#permalink]

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05 Oct 2018, 22:42
5
00:00

Difficulty:

35% (medium)

Question Stats:

59% (01:35) correct 41% (02:52) wrong based on 27 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

Attachment:

GC.jpg [ 13.41 KiB | Viewed 467 times ]

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Re: A square with a side of 5 is positioned with its Corner in the center  [#permalink]

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05 Oct 2018, 23:10
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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Senior DS Moderator
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Re: A square with a side of 5 is positioned with its Corner in the center  [#permalink]

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05 Oct 2018, 23:12
OA = C, provide your explanation

warrior1991 wrote:
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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Re: A square with a side of 5 is positioned with its Corner in the center  [#permalink]

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05 Oct 2018, 23:40
1
Please let me know if there is any easy way for solving this question.
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IMG_8151.JPG [ 1.9 MiB | Viewed 371 times ]

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Re: A square with a side of 5 is positioned with its Corner in the center  [#permalink]

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05 Oct 2018, 23:42
Bunuel

Sir what are your thoughts on this?? How should we approach to this question??
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Re: A square with a side of 5 is positioned with its Corner in the center  [#permalink]

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05 Oct 2018, 23:43
gmatbusters wrote:
OA = C, provide your explanation

warrior1991 wrote:
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.

By the way, what is the source of this question??
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Intern
Joined: 20 Jun 2018
Posts: 17
Re: A square with a side of 5 is positioned with its Corner in the center  [#permalink]

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06 Oct 2018, 00:08
1
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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Re: A square with a side of 5 is positioned with its Corner in the center  [#permalink]

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06 Oct 2018, 00:16
Mike03 wrote:
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/

Thanks for sharing !! Completely surprised by this!! It was so easy after seeing the video in your link !!!
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Re: A square with a side of 5 is positioned with its Corner in the center  [#permalink]

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06 Oct 2018, 00:32
1

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 303 times ]

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Re: A square with a side of 5 is positioned with its Corner in the center  [#permalink]

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06 Oct 2018, 09:03
1
gmatbusters wrote:

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

Attachment:
The attachment GC.jpg is no longer available

I followed this approach -
Attachments

WhatsApp Image 2018-10-06 at 9.31.35 PM.jpeg [ 32.02 KiB | Viewed 248 times ]

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Re: A square with a side of 5 is positioned with its Corner in the center  [#permalink]

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06 Oct 2018, 21:50
C) Very nice

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Re: A square with a side of 5 is positioned with its Corner in the center &nbs [#permalink] 06 Oct 2018, 21:50
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