Find all School-related info fast with the new School-Specific MBA Forum

It is currently 27 Jun 2016, 16:09
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Is the measure of one of the interior angles of

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

Hide Tags

Director
Director
avatar
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 538
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 63

Kudos [?]: 2255 [0], given: 217

Is the measure of one of the interior angles of [#permalink]

Show Tags

New post 07 Feb 2012, 18:01
9
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

41% (01:55) correct 59% (00:58) wrong based on 269 sessions

HideShow timer Statistics

Is the measure of one of the interior angles of quadrilateral ABCD equal to 60 degrees?

(1) Two of the interior angles of ABCD are right angles.
(2) The degree measure of angle ABC is twice the degree measure of angle BCD

[Reveal] Spoiler:
As the OA is not given, I have gone for answer C and this is how I reached. Please let me know whether I am right.

First, we know that the sum of 4 angles of a quadrilateral is 360 degrees.

Now, considering statement 1

Two angles are right angles. Not sufficient as it doesn't say anything about the other two angles.

Considering Statement 2

Not sufficient as it doesn't say anything about the other two angles.

Combining both statements

We can find the 4th angle as below

90+90+90+x = 360
270+x = 360
x = 90. where x is the 4th angle. So the answer is NO the angle won't be 60 degrees.
[Reveal] Spoiler: OA

_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730


Last edited by Bunuel on 18 Sep 2012, 00:48, edited 3 times in total.
Edited the OA
Expert Post
9 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 33528
Followers: 5938

Kudos [?]: 73635 [9] , given: 9903

Re: Quadrilateral ABCD [#permalink]

Show Tags

New post 07 Feb 2012, 18:07
9
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
Is the measure of one of the interior angles of quadrilateral ABCD equal to 60?

Sum of inner angels of quadrilateral is 360 degrees. (Sum of inner angles of polygon=180*(n-2), where n is # of sides)

(1) Two of the interior angles of ABCD are right angles --> angles can be 90+90 + any combination of two angels totaling 180. Not sufficient.

(2) The degree measure of angle ABC is twice the degree measure of angle BCD --> <ABC=2<BCD. Not sufficient

(1)+(2) Angles can be 90+90+45+135 Or 90+90+60+120. Not sufficient.

Answer: E.
_________________

New to the Math Forum?
Please read this: 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

Intern
Intern
avatar
Joined: 03 Feb 2012
Posts: 9
Followers: 0

Kudos [?]: 2 [0], given: 7

Re: Is the measure of one of the interior angles of [#permalink]

Show Tags

New post 07 Feb 2012, 23:25
That question was a tricky sucker.
Intern
Intern
avatar
Joined: 07 Aug 2012
Posts: 26
Location: United States
Concentration: Finance, Strategy
GMAT 1: 710 Q50 V35
GPA: 3.7
WE: Consulting (Insurance)
Followers: 0

Kudos [?]: 8 [0], given: 3

Trignometry [#permalink]

Show Tags

New post 17 Sep 2012, 21:35
Is the measure of one of the interior angles of quadrilateral ABCD equal to 60 degrees?
(1) Two of the interior angles of ABCD are right angles.
(2) The degree measure of angle ABC is twice the degree measure of angle BCD.

A. Statement (1) ALONEis sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONEis sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHERare sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

My approach to the problem :

Each statement individually cannot help solve the question. Using combined information from two statements:

It isn't clear from combined information whether angle BCD is right angle. So two cases arises here.

Case 1: If angle BCD is not the a right angle. In this case Angle ABC is 60 degrees since ABC + BCD = 180 degress as sum of other two angles of quadrilateral is 180 degress.

Case 2: If angle BCD is the right angle. In this case angle ABC is 45 degrees and other angles of quadrilateral are 90 and 135 degrees.

So we cannot clearly say that angle ABC is 60 with both information combined and so my answer to this is E but the official answer is otherwise.

Please correct if my logic is incorrect.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 33528
Followers: 5938

Kudos [?]: 73635 [0], given: 9903

Re: Trignometry [#permalink]

Show Tags

New post 18 Sep 2012, 00:50
Expert's post
dineesha wrote:
Is the measure of one of the interior angles of quadrilateral ABCD equal to 60 degrees?
(1) Two of the interior angles of ABCD are right angles.
(2) The degree measure of angle ABC is twice the degree measure of angle BCD.

A. Statement (1) ALONEis sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONEis sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHERare sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

My approach to the problem :

Each statement individually cannot help solve the question. Using combined information from two statements:

It isn't clear from combined information whether angle BCD is right angle. So two cases arises here.

Case 1: If angle BCD is not the a right angle. In this case Angle ABC is 60 degrees since ABC + BCD = 180 degress as sum of other two angles of quadrilateral is 180 degress.

Case 2: If angle BCD is the right angle. In this case angle ABC is 45 degrees and other angles of quadrilateral are 90 and 135 degrees.

So we cannot clearly say that angle ABC is 60 with both information combined and so my answer to this is E but the official answer is otherwise.

Please correct if my logic is incorrect.


Merging similar topics. please refer to the solution above.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html
_________________

New to the Math Forum?
Please read this: 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

Manager
Manager
avatar
Joined: 18 May 2010
Posts: 80
Followers: 0

Kudos [?]: 1 [0], given: 45

Re: Is the measure of one of the interior angles of [#permalink]

Show Tags

New post 06 Oct 2012, 06:30
Since two angles of the quad. are right angles, would other angles not be right angles as well? As sides emanating from right angles would only be straight, and hence the corresponding angles will also be right angles? Correct me if I am wrong. Thx.
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 33528
Followers: 5938

Kudos [?]: 73635 [1] , given: 9903

Re: Is the measure of one of the interior angles of [#permalink]

Show Tags

New post 06 Oct 2012, 06:49
1
This post received
KUDOS
Expert's post
chigiwigi wrote:
Since two angles of the quad. are right angles, would other angles not be right angles as well? As sides emanating from right angles would only be straight, and hence the corresponding angles will also be right angles? Correct me if I am wrong. Thx.


Consider the diagram below:
Attachment:
Trapezoid.png
Trapezoid.png [ 1.62 KiB | Viewed 6545 times ]
As you can see we can have a quadrilateral with only two right angles.

Hope it helps.
_________________

New to the Math Forum?
Please read this: 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

Manager
Manager
avatar
Joined: 18 May 2010
Posts: 80
Followers: 0

Kudos [?]: 1 [0], given: 45

Re: Is the measure of one of the interior angles of [#permalink]

Show Tags

New post 06 Oct 2012, 07:31
ok, makes sense. Thanks.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 10214
Followers: 481

Kudos [?]: 124 [0], given: 0

Premium Member
Re: Is the measure of one of the interior angles of [#permalink]

Show Tags

New post 28 Jul 2014, 08:52
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 10214
Followers: 481

Kudos [?]: 124 [0], given: 0

Premium Member
Re: Is the measure of one of the interior angles of [#permalink]

Show Tags

New post 09 Oct 2015, 10:50
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Intern
Intern
avatar
Joined: 04 Apr 2015
Posts: 38
Followers: 1

Kudos [?]: 1 [0], given: 1233

Re: Is the measure of one of the interior angles of [#permalink]

Show Tags

New post 25 Dec 2015, 02:07
Bunuel wrote:
Is the measure of one of the interior angles of quadrilateral ABCD equal to 60?

Sum of inner angels of quadrilateral is 360 degrees. (Sum of inner angles of polygon=180*(n-2), where n is # of sides)

(1) Two of the interior angles of ABCD are right angles --> angles can be 90+90 + any combination of two angels totaling 180. Not sufficient.

(2) The degree measure of angle ABC is twice the degree measure of angle BCD --> <ABC=2<BCD. Not sufficient

(1)+(2) Angles can be 90+90+45+135 Or 90+90+60+120. Not sufficient.

Answer: E.




Hi bunuel

i believe answer should be C
90-90-120-60

Both A & B will result in only above sequence
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 33528
Followers: 5938

Kudos [?]: 73635 [0], given: 9903

Re: Is the measure of one of the interior angles of [#permalink]

Show Tags

New post 25 Dec 2015, 05:49
Expert's post
varundixitmro2512 wrote:
Bunuel wrote:
Is the measure of one of the interior angles of quadrilateral ABCD equal to 60?

Sum of inner angels of quadrilateral is 360 degrees. (Sum of inner angles of polygon=180*(n-2), where n is # of sides)

(1) Two of the interior angles of ABCD are right angles --> angles can be 90+90 + any combination of two angels totaling 180. Not sufficient.

(2) The degree measure of angle ABC is twice the degree measure of angle BCD --> <ABC=2<BCD. Not sufficient

(1)+(2) Angles can be 90+90+45+135 Or 90+90+60+120. Not sufficient.

Answer: E.




Hi bunuel

i believe answer should be C
90-90-120-60

Both A & B will result in only above sequence


The post you quote has TWO possible cases. Please re-read the solution.
_________________

New to the Math Forum?
Please read this: 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

Senior Manager
Senior Manager
avatar
Joined: 29 Oct 2013
Posts: 289
Concentration: Finance
Schools: Cornell AMBA'17
GMAT 1: 750 Q V46
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Followers: 13

Kudos [?]: 312 [0], given: 189

GMAT ToolKit User
Re: Is the measure of one of the interior angles of [#permalink]

Show Tags

New post 18 Jan 2016, 08:43
the source of this question is gmatprep and not kaplan
_________________

Please consider giving 'kudos' if you like my post and want to thank :)

My journey V46 and 750 -> my-journey-to-46-on-verbal-750overall-171722.html#p1367876

Expert Post
Math Revolution GMAT Instructor
User avatar
Joined: 16 Aug 2015
Posts: 1390
GPA: 3.82
Followers: 87

Kudos [?]: 687 [0], given: 0

Premium Member
Re: Is the measure of one of the interior angles of [#permalink]

Show Tags

New post 18 Jan 2016, 22:13
Expert's post
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is the measure of one of the interior angles of quadrilateral ABCD equal to 60 degrees?

(1) Two of the interior angles of ABCD are right angles.
(2) The degree measure of angle ABC is twice the degree measure of angle BCD

In the original condition, there are 4 variables(A,B,C,D) and 1 equation(A+B+C+D=180), which should match with the number of equations. So you need 3 more equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer. When 1) & 2)
Attachment:
GCDS enigma123      Is the measure of one of the interior (20160119).jpg
GCDS enigma123 Is the measure of one of the interior (20160119).jpg [ 1.78 MiB | Viewed 1209 times ]

Just like the above, there are both yes and no, which is not sufficient. Therefore, the answer is E.


-> For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Re: Is the measure of one of the interior angles of   [#permalink] 18 Jan 2016, 22:13
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic What is the measure of angle B? Bunuel 4 22 Apr 2015, 03:34
Experts publish their posts in the topic Is the measure of one of the interior angles of quadrilatera imadkho 1 18 Mar 2012, 06:56
Is the measure of one of the interior angles of a cyclic meghash3 5 28 May 2010, 09:28
15 Experts publish their posts in the topic Is the measure of one of the interior angles of quadrilatera kt00381n 16 01 Nov 2009, 13:08
6 Experts publish their posts in the topic Is the measure of one of the interior angles of quadrilateral ABCD japped187 9 30 May 2008, 06:21
Display posts from previous: Sort by

Is the measure of one of the interior angles of

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


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.