GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 24 Jan 2019, 00:41

### 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

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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### Key Strategies to Master GMAT SC

January 26, 2019

January 26, 2019

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
• ### Free GMAT Number Properties Webinar

January 27, 2019

January 27, 2019

07:00 AM PST

09:00 AM PST

Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.

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

Author Message
TAGS:

### Hide Tags

Current Student
Status: It always seems impossible until it's done!!
Joined: 29 Aug 2012
Posts: 1118
Location: India
WE: General Management (Aerospace and Defense)
What is the area of the region in which squares ABCD and EFGH overlap?  [#permalink]

### Show Tags

16 Jun 2014, 20:51
1
4
00:00

Difficulty:

55% (hard)

Question Stats:

54% (01:41) correct 46% (01:39) wrong based on 182 sessions

### HideShow timer Statistics

Attachment:

Problem.JPG [ 12.34 KiB | Viewed 2716 times ]
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 $$2\sqrt{2}$$.

_________________
Director
Joined: 25 Apr 2012
Posts: 682
Location: India
GPA: 3.21
Re: What is the area of the region in which squares ABCD and EFGH overlap?  [#permalink]

### Show Tags

16 Jun 2014, 21:42
Gnpth wrote:
What is the area of the region in which squares ABCD and EFGH overlap?

STATEMENT 1:

EF bisects BC.

STATEMENT 2:

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

Quote:
Image Attached

St 1 says: EF bisects BC. Let the Point of intersection be X. Thus we have BX+XC=BC. If CX=a then EY= b where Y is the pt of intersection between EH and CD.
Now we can say EY=XC=a but we don't know if EY is equal to CX or not.Thus we cannot find length of Square EFGH

St 2 says : CE is $$2\sqrt{2}$$ and the distance from point C to point F is [m]2\sqrt{2}

Consider triangle ECX where X is the point of intersection of BC and EF...We will get a triangle with angles 45:45:90...and thus we can find CX=2 and EX=2...Implying EXCY is a square. We can get the answer.

So B
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Intern
Joined: 08 Nov 2013
Posts: 37
GMAT 1: 730 Q50 V40
Re: What is the area of the region in which squares ABCD and EFGH overlap?  [#permalink]

### Show Tags

30 Sep 2014, 02:44
How did you deduce that triangle ECX is a 45:45:90 triangle?

WoundedTiger wrote:
Gnpth wrote:
What is the area of the region in which squares ABCD and EFGH overlap?

STATEMENT 1:

EF bisects BC.

STATEMENT 2:

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

Quote:
Image Attached

St 1 says: EF bisects BC. Let the Point of intersection be X. Thus we have BX+XC=BC. If CX=a then EY= b where Y is the pt of intersection between EH and CD.
Now we can say EY=XC=a but we don't know if EY is equal to CX or not.Thus we cannot find length of Square EFGH

St 2 says : CE is $$2\sqrt{2}$$ and the distance from point C to point F is [m]2\sqrt{2}

Consider triangle ECX where X is the point of intersection of BC and EF...We will get a triangle with angles 45:45:90...and thus we can find CX=2 and EX=2...Implying EXCY is a square. We can get the answer.

So B
Manager
Status: PLAY HARD OR GO HOME
Joined: 25 Feb 2014
Posts: 147
Location: India
Concentration: General Management, Finance
Schools: Mannheim
GMAT 1: 560 Q46 V22
GPA: 3.1
Re: What is the area of the region in which squares ABCD and EFGH overlap?  [#permalink]

### Show Tags

08 Oct 2014, 02:06
Well,i doubt whether v can prove if 45-45-90 is possible here..

A is clearly insufficient.

stmnt B=
let midpt of BC be - x

Hence, BX=BC=2 ----- GIVEN
Now,as triangle EXC is right angled,and as we know the 2 given sides of that triangle we can find Side EX...

Now,let Y be point on side DC...if we observe EY has length similar to that of XC..We can clearly say that EY=XC=2..

Therefore, as we know that triangle EYC is right angled and as we know 2 sides,by using pythagoras,we can find the remaining side..

hence we have found the values of all sides,we can find its area..
_________________

ITS NOT OVER , UNTIL I WIN ! I CAN, AND I WILL .PERIOD.

Retired Moderator
Joined: 26 Nov 2012
Posts: 592
Re: What is the area of the region in which squares ABCD and EFGH overlap?  [#permalink]

### Show Tags

04 Aug 2016, 16:27
Gnpth wrote:
Attachment:
Problem.JPG
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 $$2\sqrt{2}$$.

Stat 1: EF bisects BC means EF is divided into two parts exactly. Then we can understand that the overlapped region is quarter of the two square. But we don't have enough information whether BC is also exactly half of EF then it would have been the quarter region of each square..Insufficient.

Stat 2: (From figure ) EF is diagonal of smaller square and value is $$2\sqrt{2}$$. Since $$2\sqrt{2}$$^2 + $$2\sqrt{2}$$^2 = 4 ( pythogarous theorem) and quarter square diagonal is half of full diagonal.

=>$$a\sqrt{2}$$ = $$2\sqrt{2}$$

a = 2. From this we can know the area of smaller square..Sufficient..

Option B is correct.
Manager
Joined: 08 Jan 2018
Posts: 224
Location: United States (ID)
GPA: 3.33
WE: Accounting (Accounting)
Re: What is the area of the region in which squares ABCD and EFGH overlap?  [#permalink]

### Show Tags

24 Jan 2018, 09:58
we must know the term "bisect" which means the line is divided into 2 equal parts. Hence, from st1, we cannot conclude much.
Re: What is the area of the region in which squares ABCD and EFGH overlap? &nbs [#permalink] 24 Jan 2018, 09:58
Display posts from previous: Sort by