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

 It is currently 17 Jul 2018, 06:47

### 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

# M18-15

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47037

### Show Tags

16 Sep 2014, 01:03
00:00

Difficulty:

85% (hard)

Question Stats:

55% (01:31) correct 45% (01:46) wrong based on 223 sessions

### HideShow timer Statistics

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

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 47037

### Show Tags

16 Sep 2014, 01:03
1
3
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.

_________________
Manager
Joined: 24 Nov 2014
Posts: 211
GMAT 1: 800 Q51 V51

### Show Tags

03 Mar 2015, 05:44
I think this question is good and helpful.
_________________

Marty Murray
GMAT Coach
m.w.murray@hotmail.com
http://infinitemindprep.com

Senior Manager
Joined: 31 Mar 2016
Posts: 400
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)

### Show Tags

16 Aug 2016, 05:48
I think this is a high-quality question and I agree with explanation.
Intern
Status: student
Affiliations: delhi university
Joined: 20 May 2014
Posts: 12
Schools: SPJ PGPM"17
WE: Accounting (Accounting)

### Show Tags

11 Sep 2016, 02:25
Bunuel wrote:
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.

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
Math Expert
Joined: 02 Sep 2009
Posts: 47037

### Show Tags

11 Sep 2016, 03:02
1
19941010 wrote:
Bunuel wrote:
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.

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.
_________________
Intern
Joined: 07 Aug 2016
Posts: 8
GMAT 1: 610 Q43 V31

### Show Tags

26 Sep 2016, 07:33
Aren't the diagonals of rectangle perpendicular bisector of each other?
Math Expert
Joined: 02 Sep 2009
Posts: 47037

### Show Tags

26 Sep 2016, 07:39
La1yaMalhotra wrote:
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.
_________________
Intern
Joined: 18 Nov 2014
Posts: 1

### Show Tags

12 Dec 2016, 17:04
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Hi, can you explain more?
Basically, total 3 angles of a triangle is 180. If <AEB = 60, total value of 3 angles in triangle AEB is 150 degree (Because <AEB = 60, <ABE= 60, and <BAE = 30). Moreover, 4 angles AEB + BEC + CED + DEA = 360. As a result, <AEB must be at least 90 degree.
Thank you so much!
Math Expert
Joined: 02 Sep 2009
Posts: 47037

### Show Tags

13 Dec 2016, 02:01
hnguyen26 wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Hi, can you explain more?
Basically, total 3 angles of a triangle is 180. If <AEB = 60, total value of 3 angles in triangle AEB is 150 degree (Because <AEB = 60, <ABE= 60, and <BAE = 30). Moreover, 4 angles AEB + BEC + CED + DEA = 360. As a result, <AEB must be at least 90 degree.
Thank you so much!

The question is fine. You just made mistake in calculations. The measure of angle BAE is 60, not 30. Please re-read the discussion more above carefully this time.
_________________
Director
Joined: 08 Jun 2015
Posts: 518
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38

### Show Tags

21 Jun 2017, 07:41
The answer is option C. Well explained above.
_________________

" The few , the fearless "

Intern
Joined: 21 May 2015
Posts: 17

### Show Tags

22 Aug 2017, 14:46
I think this is a high-quality question and I agree with explanation.
Intern
Joined: 15 Jan 2014
Posts: 1

### Show Tags

04 Nov 2017, 02:22
Can you please explain the angle measure 2x for EBA
Math Expert
Joined: 02 Sep 2009
Posts: 47037

### Show Tags

04 Nov 2017, 03:14
vishalkss wrote:
Can you please explain the angle measure 2x for EBA

We denoted $$\angle EAD$$ as x. The stem says that angle $$ABD$$ is twice angle $$EAD$$, so it's 2x (notice that EBA and ABD are the same angle).
_________________
Re: M18-15   [#permalink] 04 Nov 2017, 03:14
Display posts from previous: Sort by

# M18-15

Moderators: chetan2u, Bunuel

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.