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

It is currently 24 Jul 2014, 05:12

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

In the figure shown, point O is the center of semicircle and

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
1 KUDOS received
VP
VP
avatar
Joined: 07 Apr 2009
Posts: 1114
Concentration: General Management, Strategy
Schools: Duke (Fuqua) - Class of 2012
Followers: 26

Kudos [?]: 320 [1] , given: 19

GMAT Tests User Premium Member
In the figure shown, point O is the center of semicircle and [#permalink] New post 17 Jul 2009, 14:00
1
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (medium)

Question Stats:

56% (01:36) correct 44% (01:21) wrong based on 79 sessions
Image

In the figure shown, point O is the center of semicircle and points B, C, and D lie on the semicircle. If the length of line segment AB is equal to the length of line segment OC, what is the degree measure of angle BAO?

(1) The degree measure of angle COD is 60
(2) The degree measure of angle BCO is 40

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-figure-shown-point-o-is-the-center-of-the-semicircle-88009.html
[Reveal] Spoiler: OA

_________________

Diversity


Last edited by Bunuel on 30 Jul 2012, 04:37, edited 2 times in total.
Edited the question and added the OA.
Kaplan Promo CodeKnewton GMAT Discount CodesGMAT Pill GMAT Discount Codes
3 KUDOS received
Current Student
User avatar
Joined: 18 Jun 2009
Posts: 361
Location: San Francisco
Schools: Duke,Oxford,IMD,INSEAD
Followers: 8

Kudos [?]: 61 [3] , given: 15

GMAT Tests User
Re: semicircle and triangle [#permalink] New post 18 Jul 2009, 07:42
3
This post received
KUDOS
alwynjoseph wrote:
asimov wrote:
hi gmanjesh, can you please help us understand why
y=2z
how do you know BAO and BOA have the same angle?

I'm assuming that's the same assumption you used to assume OBC and OCB are equal.

Hi Asimov

triangle ABO is isoceles with OB and AB are equal sides, hence the opposite angles BAO and BOA are equal


thanks alwynjoseph for explaining it

Asimov OB and OC are the radius and hence they are euqal and as per the question AB=OC therefore AB=OC=OB
2 KUDOS received
Intern
Intern
avatar
Joined: 23 May 2010
Posts: 2
Followers: 0

Kudos [?]: 2 [2] , given: 1

Re: semicircle and triangle [#permalink] New post 23 May 2010, 15:25
2
This post received
KUDOS
ok I found out why y = 2z.

If angle BAO = x, then angle BOA = x (because triangle BAO is Isosceles)

Therefore, angle ABO = 180 - 2x (because the sum of all the angles of the triangle is 180)

Since line segment AC is a straight line that means ABO + CBO = 180.

If you substitute

ABO = 180 - 2x

into

ABO + CBO = 180

CBO = 2x. Then BOC = 180 - 4x. (because triangle BOC is isosceles)
2 KUDOS received
Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 2049
Followers: 125

Kudos [?]: 875 [2] , given: 376

GMAT Tests User
Re: semicircle and triangle [#permalink] New post 04 May 2011, 08:25
2
This post received
KUDOS
asimov wrote:
In the figure shown, point O is the center of semicircle and points B, C, and D lie on the semicircle. If the length of line segment AB is equal to the length of line segment OC, what is the degree measure of angle BAO?
(1) The degree measure of angle COD is 60
(2) The degree measure of angle BCO is 40
[Reveal] Spoiler: Official Answer
D


Sol:

Please find image herewith attached.

Attachment:
Semicircle_And_Triangle.PNG
Semicircle_And_Triangle.PNG [ 12.23 KiB | Viewed 5605 times ]



From the stem:
AB=OC=OB=Radius
Thus, ABO and BOC are both isosceles triangles.


m\angle{BAO}=m\angle{BOA}=x^{\circ} [Note: OB=AB]

m\angle{OBC}=m\angle{OCB}=y^{\circ} [Note: OB=OC]

Theorem:
An exterior angle of a triangle is equal to the sum of its interior opposite angles.

m\angle{CBO}=m\angle{BAO}+m\angle{BOA}

y=x+x=2x----------------------1


Q: What is x?

1.
\angle{COD}=60^{\circ}=t

Theorem:
Sum of three angles of a triangle is 180^{\circ}

m\angle{OCB}+m\angle{OBC}+m\angle{COB}=180

y+y+z=180

z=180-2y---------------------2

Using 1 and 2:

z=180-2(2x)

z=180-4x-----------------3

Theorem:
Angles on one side of a straight line will always add to 180^{\circ}

m\angle{COD}+m\angle{BOA}+m\angle{COB}=180^{\circ}

60+x+z=180

z=120-x----------------4

Using equations 3 and 4:

180-4x=120-x

3x=60

x=20^{\circ}

Sufficient.

2.

m\angle{OCB}=40^{\circ}=y=m\angle{CBO}

y=40^{\circ} ----------------------5

Using 1 and 5:

2x=40

x=20

Sufficient.

Ans: "D"

_________________

~fluke

Get the best GMAT Prep Resources with GMAT Club Premium Membership

1 KUDOS received
Current Student
User avatar
Joined: 18 Jun 2009
Posts: 361
Location: San Francisco
Schools: Duke,Oxford,IMD,INSEAD
Followers: 8

Kudos [?]: 61 [1] , given: 15

GMAT Tests User
Re: semicircle and triangle [#permalink] New post 17 Jul 2009, 14:37
1
This post received
KUDOS
Assume angle OBC=y and angle BAO=z

Using (1)
=========
y = 2z ---(i)(exterior angle is sum of opp interior angles)

z+(180-2y)+60=180 ---(ii) (sum of angle AOB, BOC and COD is 180)
Solving (i) and (ii) we get z=20
Hence sufficient

Using (2)
=========
Angle BCO = y = 40
==> z=40/2 = 20
Hence sufficient

Answer (D).
1 KUDOS received
Manager
Manager
avatar
Joined: 17 Dec 2007
Posts: 106
Followers: 0

Kudos [?]: 49 [1] , given: 8

Re: semicircle and triangle [#permalink] New post 17 Jul 2009, 14:38
1
This post received
KUDOS
asimov wrote:
Image

In the figure shown, point O is the center of semicircle and points B, C, and D lie on the semicircle. If the length of line segment AB is equal to the length of line segment OC, what is the degree measure of angle BAO?

(1) The degree measure of angle COD is 60
(2) The degree measure of angle BCO is 40




I think 2 alone is sufficient

Given data : AB = OC which implies = BO.

So In triangle ABO, AB = BO , isoceles triangle hence opposite angles BOA =angle BAO
similarly triangle

We know BO=OC and hence triangle BOC is also isoceles. So if angle BCO = 40, then angle OBC =40 and hence angle ABO = 180-40 = 120



once angle ABO is known, we know angle BOA = BAO, hence 2 angle BAO+ angle ABO = 180
2 BAO = 60 and hence BAO is 30
1 KUDOS received
Manager
Manager
avatar
Joined: 17 Dec 2007
Posts: 106
Followers: 0

Kudos [?]: 49 [1] , given: 8

Re: semicircle and triangle [#permalink] New post 18 Jul 2009, 07:25
1
This post received
KUDOS
asimov wrote:
hi gmanjesh, can you please help us understand why
y=2z
how do you know BAO and BOA have the same angle?

I'm assuming that's the same assumption you used to assume OBC and OCB are equal.

Hi Asimov

triangle ABO is isoceles with OB and AB are equal sides, hence the opposite angles BAO and BOA are equal
Expert Post
VP
VP
avatar
Joined: 07 Apr 2009
Posts: 1114
Concentration: General Management, Strategy
Schools: Duke (Fuqua) - Class of 2012
Followers: 26

Kudos [?]: 320 [0], given: 19

GMAT Tests User Premium Member
Re: semicircle and triangle [#permalink] New post 18 Jul 2009, 06:32
Expert's post
hi gmanjesh, can you please help us understand why
y=2z
how do you know BAO and BOA have the same angle?

I'm assuming that's the same assumption you used to assume OBC and OCB are equal.
_________________

Diversity

Expert Post
VP
VP
avatar
Joined: 07 Apr 2009
Posts: 1114
Concentration: General Management, Strategy
Schools: Duke (Fuqua) - Class of 2012
Followers: 26

Kudos [?]: 320 [0], given: 19

GMAT Tests User Premium Member
Re: semicircle and triangle [#permalink] New post 18 Jul 2009, 08:17
Expert's post
thanks a lot. I didn't catch on the radius -> isoceles triangle. it makes sense to me now.

the OA is D
_________________

Diversity

Intern
Intern
avatar
Joined: 20 Jul 2009
Posts: 1
Followers: 0

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

Re: semicircle and triangle [#permalink] New post 20 Jul 2009, 04:05
Hi, guys. If I follow your explanation correctly, I think you're assuming that AC is a straight line and that ACO is a triangle.

If that is what you're doing, is there anything in the question setup that says we can assume that AC is a straight line?

Thanks.
Senior Manager
Senior Manager
User avatar
Joined: 21 Jul 2009
Posts: 266
Location: New York, NY
Followers: 1

Kudos [?]: 35 [0], given: 23

GMAT Tests User
Re: semicircle and triangle [#permalink] New post 27 Aug 2009, 12:24
gmanjesh wrote:

y = 2z ---(i)(exterior angle is sum of opp interior angles)


I don't understand this part. Is anyone able to illustrate please?
Intern
Intern
avatar
Joined: 14 Apr 2010
Posts: 5
Followers: 0

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

Re: semicircle and triangle [#permalink] New post 21 Apr 2010, 18:09
I understand how statement II is sufficient, but I am having a hard time with statement I. Can someone please help me out?

One thing that seems unexplained with the statement I work done thus far:

I agree that angle BAO = BOA, but in superman's equation he assumed that angle BOC = BOA. How do we know that?
Manhattan GMAT Instructor
User avatar
Joined: 27 Aug 2009
Posts: 153
Location: St. Louis, MO
Schools: Cornell (Bach. of Sci.), UCLA Anderson (MBA)
Followers: 125

Kudos [?]: 196 [0], given: 6

Re: semicircle and triangle [#permalink] New post 19 Jun 2010, 09:03
grifter000 wrote:
Hi, guys. If I follow your explanation correctly, I think you're assuming that AC is a straight line and that ACO is a triangle.

If that is what you're doing, is there anything in the question setup that says we can assume that AC is a straight line?

Thanks.

Good general question. You should almost assume that DS diagrams are not drawn to scale. But there are things about the picture that you can take as fact:

(1) If two lines look like they meet, they do. (i.e. no microscopic gaps)
(2) If a line looks straight, it is. (i.e. no trick angles of 179.99 degrees)
_________________


Emily Sledge | Manhattan GMAT Instructor | St. Louis

Manhattan GMAT Discount | Manhattan GMAT Course Reviews | Manhattan GMAT Reviews

Director
Director
User avatar
Joined: 24 Aug 2007
Posts: 956
WE 1: 3.5 yrs IT
WE 2: 2.5 yrs Retail chain
Followers: 51

Kudos [?]: 668 [0], given: 40

GMAT Tests User
Re: semicircle and triangle [#permalink] New post 22 Jun 2010, 10:33
IMO D.

This is simple test of triangle basics. Thanks for sharing this question.
_________________

Want to improve your CR: cr-methods-an-approach-to-find-the-best-answers-93146.html
Tricky Quant problems: 50-tricky-questions-92834.html
Important Grammer Fundamentals: key-fundamentals-of-grammer-our-crucial-learnings-on-sc-93659.html

Manager
Manager
avatar
Joined: 30 Mar 2010
Posts: 84
GMAT 1: 730 Q48 V42
Followers: 0

Kudos [?]: 8 [0], given: 5

GMAT Tests User
Re: semicircle and triangle [#permalink] New post 26 Nov 2010, 07:15
Ok so I understand that BOA = BAO and if BOA = 2z then OBC = z. But I thought that given that OC = AB = OB then BOA = BAO = OBC?

Where is my mistake??
Manager
Manager
avatar
Joined: 03 Jun 2009
Posts: 50
Followers: 0

Kudos [?]: 1 [0], given: 7

Re: semicircle and triangle [#permalink] New post 27 Nov 2010, 07:42
superman wrote:
Assume angle OBC=y and angle BAO=z

Using (1)
=========
y = 2z ---(i)(exterior angle is sum of opp interior angles)

z+(180-2y)+60=180 ---(ii) (sum of angle AOB, BOC and COD is 180)
Solving (i) and (ii) we get z=20
Hence sufficient

Using (2)
=========
Angle BCO = y = 40
==> z=40/2 = 20
Hence sufficient

Answer (D).


Gud Xplanation Superman!!! Kudos +1
Manager
Manager
User avatar
Joined: 18 Sep 2010
Posts: 60
Followers: 2

Kudos [?]: 17 [0], given: 303

Re: semicircle and triangle [#permalink] New post 04 May 2011, 08:46
woooow!
fluke, your solution is very helpful
thank you so much! :-D
_________________

(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Manager
Manager
User avatar
Joined: 11 Jul 2009
Posts: 147
WE: Design (Computer Software)
Followers: 1

Kudos [?]: 16 [0], given: 18

GMAT ToolKit User CAT Tests
Re: semicircle and triangle [#permalink] New post 06 May 2011, 08:00
each statement alone is sufficient, so... D
_________________

Kaustubh

Re: semicircle and triangle   [#permalink] 06 May 2011, 08:00
    Similar topics Author Replies Last post
Similar
Topics:
22 Experts publish their posts in the topic In the figure shown, point O is the center of the semicircle msunny 18 19 Dec 2009, 07:28
3 Experts publish their posts in the topic In the figure shown, point O is the center of the semicircle burnttwinky 6 15 Dec 2009, 12:09
2 Experts publish their posts in the topic In the figure shown, point O is the center of the semicircle DenisSh 7 04 Oct 2009, 22:22
5 In the figure shown, point O is the center of the semicircle marcodonzelli 8 10 Mar 2008, 10:43
1 In the figure shown, point O is the center of the semicircle dinesh8 2 01 Jun 2006, 21:17
Display posts from previous: Sort by

In the figure shown, point O is the center of semicircle and

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| 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®.