Last visit was: 19 Nov 2025, 01:02 It is currently 19 Nov 2025, 01:02
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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
655-705 Level|   Geometry|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,379
Own Kudos:
778,161
 [16]
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,379
Kudos: 778,161
 [16]
What is the area of the region in which squares ABCD and EFGH overlap? 04 Dec 2019, 02:42
Kudos
Add Kudos
15
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

56% (01:41) correct 44% (01:43) wrong based on 318 sessions

History

Date
Time
Result
Not Attempted Yet

What is the area of the region in which squares ABCD and EFGH overlap?

(1) EF bisects BC.

(2) The distance from point C to point E is \(2\sqrt{2}\) and the distance from point C to point F is \(2\sqrt{2}\).


Are You Up For the Challenge: 700 Level Questions

Show Spoiler
Attachment:
Problem.JPG
Problem.JPG [ 4.75 KiB | Viewed 7018 times ]
ShowHide Answer
Official Answer
B
User avatar
nick1816
User avatar
Retired Moderator
Joined: 19 Oct 2018
Last visit: 06 Nov 2025
Posts: 1,849
Own Kudos:
8,237
 [3]
Given Kudos: 707
Location: India
Posts: 1,849
Kudos: 8,237
 [3]
What is the area of the region in which squares ABCD and EFGH overlap? 04 Dec 2019, 12:50
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Tricky one!!

Statement 1- Length of OC =2 cm

But length of OE can vary. (see the figure below for statement 1)

Insufficient

Statement 2-

Case 1- When AB is parallel to EF

OEKC is a square with sides 2cm

Area= 4cm^2

Case 2- When AB is not parallel to EF

Draw perpendicular CJ and CI on EF and EH respectively

CJ=CI=2cm
Angle ICL= Angle JCK

Hence triangle LIC is congruent to triangle KJC. Both triangles have equal areas

Overlapped area EKCL= Area of JCIE= 2*2=4cm^2

Sufficient

B



Bunuel

What is the area of the region in which squares ABCD and EFGH overlap?

(1) EF bisects BC.

(2) The distance from point C to point E is \(2\sqrt{2}\) and the distance from point C to point F is \(2\sqrt{2}\).


Are You Up For the Challenge: 700 Level Questions

Show Spoiler
Attachment:
The attachment Problem.JPG is no longer available
Show more

Attachments

Untitled.png
Untitled.png [ 3.86 KiB | Viewed 6463 times ]

Capture1.PNG
Capture1.PNG [ 7.89 KiB | Viewed 6445 times ]

avatar
ShaliniShalini
avatar
Joined: 05 Aug 2019
Last visit: 20 Oct 2021
Posts: 11
Own Kudos:
3
Given Kudos: 9
Posts: 11
Kudos: 3
What is the area of the region in which squares ABCD and EFGH overlap? 08 Dec 2019, 18:54
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Can't understand S2. Can someone please explain this?
User avatar
Aviral1995
User avatar
Current Student
Joined: 13 Apr 2019
Last visit: 23 May 2022
Posts: 233
Own Kudos:
68
 [1]
Given Kudos: 309
Location: India
Schools: McDonough'23 (II) Mendoza'23 (A$) Kelley '23 (A$) Schulich Sept '23 (WA)
GMAT 1: 710 Q49 V36
GPA: 3.85
Products:
My Reviews
Schools: McDonough'23 (II) Mendoza'23 (A$) Kelley '23 (A$) Schulich Sept '23 (WA)
GMAT 1: 710 Q49 V36
Posts: 233
Kudos: 68
 [1]
What is the area of the region in which squares ABCD and EFGH overlap? 12 Dec 2019, 05:41
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ShaliniShalini
Can't understand S2. Can someone please explain this?
Show more

ShaliniShalini

If we look at S2: it says distance of point C from point E and F is same and is equal to 2 root2

It means C is the center of the square EFGH. We are also given that side of square EFGH is 4

So, we can easily get the side of the small square asked; since we know the size of it now(which is 2)

Hope this helps!
avatar
ism1994
avatar
Joined: 09 Nov 2020
Last visit: 13 Dec 2020
Posts: 12
Own Kudos:
8
Given Kudos: 1
Posts: 12
Kudos: 8
What is the area of the region in which squares ABCD and EFGH overlap? 26 Nov 2020, 00:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi all,

Can someone please explain why B alone is correct?

IMO B means that the EFGH square is hinged in C, but it still can rotate around it (thus giving different areas while superposing with ABCD, right?).

If EFGH is both blocked in translation and rotation (i.e., 1+2) then we can draw conclusions on the overlapping region --> Ans C
User avatar
Fdambro294
User avatar
Joined: 10 Jul 2019
Last visit: 20 Aug 2025
Posts: 1,350
Own Kudos:
741
Given Kudos: 1,656
Posts: 1,350
Kudos: 741
What is the area of the region in which squares ABCD and EFGH overlap? 23 Jun 2021, 00:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
nick1816 has the best explanation above.

Follow his picture underneath his explanation.


Statement 2:

Because we are given that EC = CF = 2 * sqrt(2)

And we know that EFGH is a square with side length of 4

Triangle ECF must be a right triangle because the sides are in the Ratio of: 1 : 1 : sqrt(2)

Or

2 * sqrt(2) : 2 * sqrt(2) : 4

Now, because we know that the diagonal of any square is = (side) * sqrt(2) ——-> we know that the full diagonal EG = (4) * sqrt(2)


Since EC and EF are (1/2) of the full diagonal of Square EFGH and we know they meet at a 90 degree angle, it must be the case that point C is the exact center of square EFGH —— because of the Rule that the Two diagonals of a square are perpendicular Bisectors of each other.

This is the only inference we can make. The next part is the tricky part.

The natural trap is to think that, in the overlap region, we have a Square around its Diagonal EC. This would mean E would have to be the center of Square ABCD. However, we can not infer that.

Since the diagrams are not drawn to scale for Data Sufficiency questions, it could be that the figure is actually more like case 2 in Nick’s diagram.


Nick proves how the Area will always equal 4.

The easiest way to think about it is to imagine 2 identical squares that have identical side lengths of 4. Square ABCD stays stationary at all times.

We attach square EFGH such that the center is thumbtacked at Vertex C. We can spin square EFGH around like a wheel of fortune (a square wheel of fortune)

If you start out with the squares perfectly perpendicular to each other:

where E is also the center of square ABCD

which means that the overlap region cuts through the midpoints of the Sides of square ABCD

And finally this overlap region is a square itself

——-> it must be the case that EC is the diagonal of the Square Overlap region.

You will then find that the side length of that square is 2 and the Area of that Square Overlap region = (2) * (2) = 4


No matter how you spin square EFGH around it’s center of Point C, the region covered by the square will never change.

You can try attaching 2 smaller pieces of square paper to see this fact visually. No matter how you spin square EFGH around it’s center C, the Overlap Region’s Area will never change.

nick1816 just goes through and proves this fact by using similar triangles.

I believe, other than following that approach, the next best way is to “visualize” why statement 2 is sufficient and the Area will always be 4.

However, you can always prove this by following his work above.


ism1994
Hi all,

Can someone please explain why B alone is correct?

IMO B means that the EFGH square is hinged in C, but it still can rotate around it (thus giving different areas while superposing with ABCD, right?).

If EFGH is both blocked in translation and rotation (i.e., 1+2) then we can draw conclusions on the overlapping region --> Ans C
Show more

Posted from my mobile device
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,584
Own Kudos:
1,079
Posts: 38,584
Kudos: 1,079
What is the area of the region in which squares ABCD and EFGH overlap? 26 Sep 2023, 04:47
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Bunuel
Math Expert
105379 posts
kingbucky
496 posts