It is currently 12 Dec 2017, 19:49

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

M18-15

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42574

Kudos [?]: 135407 [0], given: 12692

M18-15 [#permalink]

Show Tags

New post 16 Sep 2014, 00:03
Expert's post
7
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

57% (01:35) correct 43% (01:48) wrong based on 175 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
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135407 [0], given: 12692

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42574

Kudos [?]: 135407 [0], given: 12692

Re M18-15 [#permalink]

Show Tags

New post 16 Sep 2014, 00:03
Expert's post
4
This post was
BOOKMARKED
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:

Image

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
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135407 [0], given: 12692

Expert Post
Manager
Manager
User avatar
G
Joined: 24 Nov 2014
Posts: 177

Kudos [?]: 239 [0], given: 21

GMAT 1: 800 Q51 V51
Re M18-15 [#permalink]

Show Tags

New post 03 Mar 2015, 04:44
I think this question is good and helpful.
_________________

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

Kudos [?]: 239 [0], given: 21

Senior Manager
Senior Manager
User avatar
Joined: 31 Mar 2016
Posts: 406

Kudos [?]: 85 [0], given: 197

Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)
GMAT ToolKit User Premium Member
Re M18-15 [#permalink]

Show Tags

New post 16 Aug 2016, 04:48
I think this is a high-quality question and I agree with explanation.

Kudos [?]: 85 [0], given: 197

Intern
Intern
avatar
Status: student
Affiliations: delhi university
Joined: 20 May 2014
Posts: 12

Kudos [?]: 6 [0], given: 49

Concentration: Finance, International Business
Schools: SPJ PGPM"17
WE: Accounting (Accounting)
GMAT ToolKit User Reviews Badge
Re: M18-15 [#permalink]

Show Tags

New post 11 Sep 2016, 01:25
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:

Image

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

Kudos [?]: 6 [0], given: 49

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42574

Kudos [?]: 135407 [1], given: 12692

Re: M18-15 [#permalink]

Show Tags

New post 11 Sep 2016, 02:02
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
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:

Image

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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135407 [1], given: 12692

Intern
Intern
avatar
B
Joined: 07 Aug 2016
Posts: 8

Kudos [?]: [0], given: 0

Re: M18-15 [#permalink]

Show Tags

New post 26 Sep 2016, 06:33
Aren't the diagonals of rectangle perpendicular bisector of each other?

Kudos [?]: [0], given: 0

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42574

Kudos [?]: 135407 [0], given: 12692

Re: M18-15 [#permalink]

Show Tags

New post 26 Sep 2016, 06:39
Expert's post
1
This post was
BOOKMARKED

Kudos [?]: 135407 [0], given: 12692

Intern
Intern
avatar
Joined: 18 Nov 2014
Posts: 1

Kudos [?]: [0], given: 1

GMAT ToolKit User
Re M18-15 [#permalink]

Show Tags

New post 12 Dec 2016, 16:04
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.
Please explain.
Thank you so much!

Kudos [?]: [0], given: 1

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42574

Kudos [?]: 135407 [0], given: 12692

Re: M18-15 [#permalink]

Show Tags

New post 13 Dec 2016, 01:01
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.
Please explain.
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135407 [0], given: 12692

Senior Manager
Senior Manager
User avatar
B
Joined: 08 Jun 2015
Posts: 341

Kudos [?]: 22 [0], given: 101

Location: India
GMAT 1: 640 Q48 V29
Re: M18-15 [#permalink]

Show Tags

New post 21 Jun 2017, 06:41
The answer is option C. Well explained above.
_________________

" The few , the fearless "

Kudos [?]: 22 [0], given: 101

Intern
Intern
avatar
B
Joined: 21 May 2015
Posts: 18

Kudos [?]: 5 [0], given: 231

GMAT ToolKit User
Re M18-15 [#permalink]

Show Tags

New post 22 Aug 2017, 13:46
I think this is a high-quality question and I agree with explanation.

Kudos [?]: 5 [0], given: 231

Intern
Intern
avatar
B
Joined: 15 Jan 2014
Posts: 1

Kudos [?]: [0], given: 1

CAT Tests
Re: M18-15 [#permalink]

Show Tags

New post 04 Nov 2017, 01:22
Can you please explain the angle measure 2x for EBA

Kudos [?]: [0], given: 1

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42574

Kudos [?]: 135407 [0], given: 12692

Re: M18-15 [#permalink]

Show Tags

New post 04 Nov 2017, 02:14

Kudos [?]: 135407 [0], given: 12692

Re: M18-15   [#permalink] 04 Nov 2017, 02:14
Display posts from previous: Sort by

M18-15

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Moderators: chetan2u, Bunuel



GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.