Last visit was: 22 Sep 2026, 10:29 It is currently 22 Sep 2026, 10:29
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
605-655 (Medium)|   Geometry|      
User avatar
GMATBusters
User avatar
GMAT Tutor
Joined: 27 Oct 2017
Last visit: 22 Sep 2026
Posts: 1,926
Own Kudos:
7,053
 [10]
Given Kudos: 244
WE:General Management (Education)
Products:
Forum Quiz
Expert
Expert reply
Posts: 1,926
Kudos: 7,053
 [10]
A square with a side of 5 is positioned with its Corner in the center 05 Oct 2018, 22:42
Kudos
Add Kudos
10
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

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

History

Date
Time
Result
Not Attempted Yet

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


Show Spoiler
Attachment:
GC.jpg
GC.jpg [ 13.41 KiB | Viewed 8107 times ]
ShowHide Answer
Official Answer
C
User avatar
warrior1991
User avatar
Joined: 03 Mar 2017
Last visit: 03 Feb 2022
Posts: 537
Own Kudos:
440
Given Kudos: 595
Location: India
Concentration: Operations, Technology
Products:
My Reviews
Posts: 537
Kudos: 440
A square with a side of 5 is positioned with its Corner in the center 05 Oct 2018, 23:10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
User avatar
GMATBusters
User avatar
GMAT Tutor
Joined: 27 Oct 2017
Last visit: 22 Sep 2026
Posts: 1,926
Own Kudos:
7,053
Given Kudos: 244
WE:General Management (Education)
Products:
Forum Quiz
Expert
Expert reply
Posts: 1,926
Kudos: 7,053
A square with a side of 5 is positioned with its Corner in the center 05 Oct 2018, 23:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Show more
User avatar
warrior1991
User avatar
Joined: 03 Mar 2017
Last visit: 03 Feb 2022
Posts: 537
Own Kudos:
440
 [2]
Given Kudos: 595
Location: India
Concentration: Operations, Technology
Products:
My Reviews
Posts: 537
Kudos: 440
 [2]
A square with a side of 5 is positioned with its Corner in the center 05 Oct 2018, 23:40
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Please let me know if there is any easy way for solving this question.
Attachments

IMG_8151.JPG
IMG_8151.JPG [ 1.9 MiB | Viewed 6945 times ]

User avatar
warrior1991
User avatar
Joined: 03 Mar 2017
Last visit: 03 Feb 2022
Posts: 537
Own Kudos:
440
Given Kudos: 595
Location: India
Concentration: Operations, Technology
Products:
My Reviews
Posts: 537
Kudos: 440
A square with a side of 5 is positioned with its Corner in the center 05 Oct 2018, 23:42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

Sir what are your thoughts on this?? How should we approach to this question??
User avatar
warrior1991
User avatar
Joined: 03 Mar 2017
Last visit: 03 Feb 2022
Posts: 537
Own Kudos:
440
Given Kudos: 595
Location: India
Concentration: Operations, Technology
Products:
My Reviews
Posts: 537
Kudos: 440
A square with a side of 5 is positioned with its Corner in the center 05 Oct 2018, 23:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Show more

By the way, what is the source of this question??
User avatar
Mike03
User avatar
Joined: 20 Jun 2018
Last visit: 17 Jun 2019
Posts: 37
Own Kudos:
34
 [2]
Given Kudos: 246
Posts: 37
Kudos: 34
 [2]
A square with a side of 5 is positioned with its Corner in the center 06 Oct 2018, 00:08
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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/
User avatar
warrior1991
User avatar
Joined: 03 Mar 2017
Last visit: 03 Feb 2022
Posts: 537
Own Kudos:
440
 [1]
Given Kudos: 595
Location: India
Concentration: Operations, Technology
Products:
My Reviews
Posts: 537
Kudos: 440
 [1]
A square with a side of 5 is positioned with its Corner in the center 06 Oct 2018, 00:16
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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/
Show more

Thanks for sharing !! Completely surprised by this!! It was so easy after seeing the video in your link !!!
User avatar
GMATBusters
User avatar
GMAT Tutor
Joined: 27 Oct 2017
Last visit: 22 Sep 2026
Posts: 1,926
Own Kudos:
7,053
 [2]
Given Kudos: 244
WE:General Management (Education)
Products:
Forum Quiz
Expert
Expert reply
Posts: 1,926
Kudos: 7,053
 [2]
A square with a side of 5 is positioned with its Corner in the center 06 Oct 2018, 00:32
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post

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 6389 times ]
User avatar
rahul16singh28
User avatar
Joined: 31 Jul 2017
Last visit: 09 Jun 2020
Posts: 428
Own Kudos:
516
 [1]
Given Kudos: 752
Location: Malaysia
Schools: INSEAD Jan '19
GPA: 3.95
WE:Consulting (Energy)
Schools: INSEAD Jan '19
Posts: 428
Kudos: 516
 [1]
A square with a side of 5 is positioned with its Corner in the center 06 Oct 2018, 09:03
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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


Show Spoiler
Attachment:
The attachment GC.jpg is no longer available
Show more

I followed this approach -
Attachments

WhatsApp Image 2018-10-06 at 9.31.35 PM.jpeg
WhatsApp Image 2018-10-06 at 9.31.35 PM.jpeg [ 32.02 KiB | Viewed 6217 times ]

avatar
Ahmadd
avatar
Joined: 06 Nov 2017
Last visit: 22 Oct 2018
Posts: 1
Posts: 1
Kudos: 0
A square with a side of 5 is positioned with its Corner in the center 06 Oct 2018, 21:50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
C) Very nice


أرسلت بواسطة iPhone بإستخدام GMAT Club Forum
User avatar
ananya1322
User avatar
Joined: 20 Jul 2025
Last visit: 07 Aug 2026
Posts: 3
Given Kudos: 73
Posts: 3
Kudos: 0
A square with a side of 5 is positioned with its Corner in the center 02 Aug 2025, 03:42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
How did we get the length of AP in the diagram? I am unable to understand
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 Sep 2026
Posts: 113,780
Own Kudos:
842,954
Given Kudos: 111,741
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,780
Kudos: 842,954
A square with a side of 5 is positioned with its Corner in the center 02 Aug 2025, 08:36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ananya1322
How did we get the length of AP in the diagram? I am unable to understand
Show more
This is a geometry question, which is not part of the GMAT Focus Edition, so you can skip it and move on.
User avatar
Aurellius
User avatar
Joined: 16 Mar 2025
Last visit: 31 Oct 2025
Posts: 14
Own Kudos:
1
Given Kudos: 9
Posts: 14
Kudos: 1
A square with a side of 5 is positioned with its Corner in the center 04 Aug 2025, 07:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Show more
User avatar
Aurellius
User avatar
Joined: 16 Mar 2025
Last visit: 31 Oct 2025
Posts: 14
Own Kudos:
1
Given Kudos: 9
Posts: 14
Kudos: 1
A square with a side of 5 is positioned with its Corner in the center 04 Aug 2025, 07:10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
Moderator:
Bunuel
Math Expert
113780 posts