Last visit was: 08 Jul 2025, 20:05 It is currently 08 Jul 2025, 20:05
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.
Close
Request Expert Reply
Confirm Cancel
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 08 Jul 2025
Posts: 102,594
Own Kudos:
739,580
 [8]
Given Kudos: 97,452
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,594
Kudos: 739,580
 [8]
Kudos
Add Kudos
8
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 08 Jul 2025
Posts: 102,594
Own Kudos:
739,580
 [5]
Given Kudos: 97,452
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,594
Kudos: 739,580
 [5]
1
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
General Discussion
User avatar
MartyTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 24 Nov 2014
Last visit: 11 Aug 2023
Posts: 3,476
Own Kudos:
5,486
 [1]
Given Kudos: 1,430
Status:Chief Curriculum and Content Architect
Affiliations: Target Test Prep
GMAT 1: 800 Q51 V51
Expert
Expert reply
GMAT 1: 800 Q51 V51
Posts: 3,476
Kudos: 5,486
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
Senthil7
Joined: 31 Mar 2016
Last visit: 05 Mar 2017
Posts: 323
Own Kudos:
Given Kudos: 197
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE:Operations (Commercial Banking)
GMAT 1: 670 Q48 V34
Posts: 323
Kudos: 210
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think this is a high-quality question and I agree with explanation.
avatar
19941010
Joined: 20 May 2014
Last visit: 05 Feb 2017
Posts: 7
Own Kudos:
Given Kudos: 49
Status:student
Affiliations: delhi university
Concentration: Finance, International Business
Schools: SPJ PGPM"17
WE:Accounting (Accounting)
Products:
Schools: SPJ PGPM"17
Posts: 7
Kudos: 7
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Official Solution:

In rectangle \(ABCD\), \(E\) is the point of intersection of diagonals. If angle \(ABD\) is twice angle \(EAD\), what is the value of angle \(CED\)?

A. 30 degrees
B. 45 degrees
C. 60 degrees
D. 90 degrees
E. 120 degrees


Look at the diagram below:



Notice that since \(\angle{BAD}=90\) degrees then \(\angle{EAB}=90-x\) degrees.

Next, since diagonals of a rectangle are equal and bisect each other then \(AE=BE\). So, \(\angle{EAB}=\angle{EBA}\): \(90-x=2x\), which gives \(x=30\). Thus, \(\angle{EAB}=\angle{EBA}=60\) and \(\angle {AEB}=60\) degrees.

Finally as \(\angle{AEB}=\angle{CED}\) then \(\angle{CED}=60\) degrees.


Answer: C


Hi,
Aren't the diagonals of a rectangle an angular bisector ? AS, WE KNOW THAT DE = BE. So, angle a should have each angle = 45 degree ? angle DAE = angle BAE = 45 ?
thanks
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 08 Jul 2025
Posts: 102,594
Own Kudos:
739,580
 [1]
Given Kudos: 97,452
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,594
Kudos: 739,580
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
19941010
Bunuel
Official Solution:

In rectangle \(ABCD\), \(E\) is the point of intersection of diagonals. If angle \(ABD\) is twice angle \(EAD\), what is the value of angle \(CED\)?

A. 30 degrees
B. 45 degrees
C. 60 degrees
D. 90 degrees
E. 120 degrees


Look at the diagram below:



Notice that since \(\angle{BAD}=90\) degrees then \(\angle{EAB}=90-x\) degrees.

Next, since diagonals of a rectangle are equal and bisect each other then \(AE=BE\). So, \(\angle{EAB}=\angle{EBA}\): \(90-x=2x\), which gives \(x=30\). Thus, \(\angle{EAB}=\angle{EBA}=60\) and \(\angle {AEB}=60\) degrees.

Finally as \(\angle{AEB}=\angle{CED}\) then \(\angle{CED}=60\) degrees.


Answer: C


Hi,
Aren't the diagonals of a rectangle an angular bisector ? AS, WE KNOW THAT DE = BE. So, angle a should have each angle = 45 degree ? angle DAE = angle BAE = 45 ?
thanks

The diagonal of a rectangle is a bisector only if the rectangle is a square.
avatar
La1yaMalhotra
Joined: 07 Aug 2016
Last visit: 11 Jun 2018
Posts: 4
GMAT 1: 610 Q43 V31
Products:
GMAT 1: 610 Q43 V31
Posts: 4
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Aren't the diagonals of rectangle perpendicular bisector of each other?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 08 Jul 2025
Posts: 102,594
Own Kudos:
Given Kudos: 97,452
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,594
Kudos: 739,580
Kudos
Add Kudos
Bookmarks
Bookmark this Post
La1yaMalhotra
Aren't the diagonals of rectangle perpendicular bisector of each other?

The diagonals of a rectangle always bisect each other but they are perpendicular to each other only if a rectangle is a square.
User avatar
spetznaz
Joined: 08 Jun 2015
Last visit: 14 Jul 2024
Posts: 255
Own Kudos:
Given Kudos: 147
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38
GPA: 3.33
Products:
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The answer is option C. Well explained above.
avatar
culsivaji
Joined: 21 May 2015
Last visit: 01 Apr 2022
Posts: 9
Own Kudos:
Given Kudos: 231
Posts: 9
Kudos: 18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think this is a high-quality question and I agree with explanation.
avatar
vishalkss
Joined: 15 Jan 2014
Last visit: 13 Feb 2021
Posts: 2
Own Kudos:
Given Kudos: 3
Location: India
Concentration: General Management, Finance
GPA: 3.4
Posts: 2
Kudos: 1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Can you please explain the angle measure 2x for EBA
User avatar
Gladiator59
Joined: 16 Sep 2016
Last visit: 05 Jul 2025
Posts: 671
Own Kudos:
Given Kudos: 192
Status:It always seems impossible until it's done.
GMAT 1: 740 Q50 V40
GMAT 2: 770 Q51 V42
Products:
GMAT 2: 770 Q51 V42
Posts: 671
Kudos: 2,456
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think this is a high-quality question and I agree with explanation. Good & helpful.
User avatar
dcummins
Joined: 14 Feb 2017
Last visit: 17 Jun 2025
Posts: 1,069
Own Kudos:
Given Kudos: 368
Location: Australia
Concentration: Technology, Strategy
GMAT 1: 560 Q41 V26
GMAT 2: 550 Q43 V23
GMAT 3: 650 Q47 V33
GMAT 4: 650 Q44 V36
GMAT 5: 600 Q38 V35
GMAT 6: 710 Q47 V41
WE:Management Consulting (Consulting)
Products:
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Good question.

I think what this brings to light are the rules of diagonals in a rectangle and the difference between the bisector of a rectangle and square.

"Each diagonal of a square is the perpendicular bisector of the other. That is, each cuts the other into two equal parts, and they cross and right angles (90°)"

Whereas, each diagonal of a rectangle bisects each other and divides the rectangle up into two equal parts, but the point at which the diagonals bisect does not create 4 equal angles.

Then, finding out what angle corresponds to what side can allow us to solve 90-x = 2x and so forth.

Thanks Bunuel
User avatar
RenanBragion
User avatar
Current Student
Joined: 01 Jun 2020
Last visit: 13 Apr 2025
Posts: 129
Own Kudos:
Given Kudos: 12
Location: Brazil
GMAT 1: 760 Q48 V46
Products:
GMAT 1: 760 Q48 V46
Posts: 129
Kudos: 13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think this is a high-quality question and I agree with explanation.
avatar
kri1311
Joined: 12 Oct 2020
Last visit: 17 Jan 2023
Posts: 48
Own Kudos:
Given Kudos: 28
Schools: HEC MiM "24
GPA: 3.8
WE:Information Technology (Computer Software)
Schools: HEC MiM "24
Posts: 48
Kudos: 32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Great points in this question:

1. The diagonal of a rectangle is a bisector only if the rectangle is a square.
2. The diagonals of a rectangle always bisect each other but they are perpendicular to each other only if a rectangle is a square.

I made the mistake of assuming the diagonal as a bisector and selected the D option.

Great explanation with great information.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 08 Jul 2025
Posts: 102,594
Own Kudos:
Given Kudos: 97,452
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,594
Kudos: 739,580
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
Moderators:
Math Expert
102594 posts
Founder
41075 posts