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

It is currently 18 Nov 2018, 12:50

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 in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
  • The winning strategy for 700+ on the GMAT

     November 20, 2018

     November 20, 2018

     06:00 PM EST

     07:00 PM EST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

As shown in the figure above, line segments AB and AC are ta

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

Hide Tags

Senior Manager
Senior Manager
User avatar
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 486
Location: India
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
As shown in the figure above, line segments AB and AC are ta  [#permalink]

Show Tags

New post 17 Jul 2014, 18:40
1
8
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

68% (02:22) correct 32% (02:20) wrong based on 130 sessions

HideShow timer Statistics

Attachment:
geometry_graphics_1.gif
geometry_graphics_1.gif [ 6.48 KiB | Viewed 3670 times ]
As shown in the figure above, line segments AB and AC are tangent to circle O. If line segments BD and DA have the same length, what is angle BAO? (Note: Figure not drawn to scale.)

A. 15º
B. 30º
C. 36º
D. 45º
E. 50º

_________________

Like my post Send me a Kudos :) It is a Good manner.
My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html

Intern
Intern
avatar
Joined: 10 Jun 2014
Posts: 24
GMAT ToolKit User
Re: As shown in the figure above, line segments AB and AC are ta  [#permalink]

Show Tags

New post 17 Jul 2014, 19:46
1
I did't think this question was easy, but I finally came up with the solution.

step 1: since AB and AC are tangent to the circle then, angles OBA = OCA =90º
step 2: Angle BAO = angle DBA = x and angle BDA = y
step 3: OB = OD (both radii of circle O) and therefore triangle BOD is isosceles so angle OBD = angle ODB =z
step 4: 2x + y = 180 , y + z =180 , x+z =90
step 5: solve both equations for variable z -> z=180-y, z = 90-x
step 6: 90-x=180-y
y-x = 90
step 7: y+2x=180
y - x = 90 (-1)
3x=90
x = 30

If someone knows a faster way to solve this question please post!
Director
Director
User avatar
S
Joined: 17 Dec 2012
Posts: 629
Location: India
As shown in the figure above, line segments AB and AC are ta  [#permalink]

Show Tags

New post Updated on: 20 Jul 2014, 18:29
It seems to me that if a line drawn from the hypotenuse of a right triangle to the opposite vertex, creates two triangles, such that one of the them is isosceles, the other has to be an isosceles or an equilateral triangle. We can easily arrive at the answer if that is the case.
_________________

Srinivasan Vaidyaraman
Sravna Holistic Solutions
http://www.sravnatestprep.com

Holistic and Systematic Approach


Originally posted by SravnaTestPrep on 17 Jul 2014, 21:37.
Last edited by SravnaTestPrep on 20 Jul 2014, 18:29, edited 1 time in total.
Manager
Manager
User avatar
Joined: 10 Feb 2014
Posts: 63
GMAT ToolKit User
Re: As shown in the figure above, line segments AB and AC are ta  [#permalink]

Show Tags

New post 20 Jul 2014, 16:49
1
a13ssandra wrote:
I did't think this question was easy, but I finally came up with the solution.

step 1: since AB and AC are tangent to the circle then, angles OBA = OCA =90º
step 2: Angle BAO = angle DBA = x and angle BDA = y
step 3: OB = OD (both radii of circle O) and therefore triangle BOD is isosceles so angle OBD = angle ODB =z
step 4: 2x + y = 180 , y + z =180 , x+z =90
step 5: solve both equations for variable z -> z=180-y, z = 90-x
step 6: 90-x=180-y
y-x = 90
step 7: y+2x=180
y - x = 90 (-1)
3x=90
x = 30

If someone knows a faster way to solve this question please post!


No need to use another variable z in step 3, apply the theorem "exterior angle = sum of opp. interior angle".
angle ODB (=OBD) = angle BAO + angle DBA = 2x
angle OBD + angle DBA = 90
\(2x + x = 90\)
\(x = 30\)
Director
Director
User avatar
S
Joined: 17 Dec 2012
Posts: 629
Location: India
Re: As shown in the figure above, line segments AB and AC are ta  [#permalink]

Show Tags

New post 20 Jul 2014, 20:30
SravnaTestPrep wrote:
It seems to me that if a line drawn from the hypotenuse of a right triangle to the opposite vertex, creates two triangles, such that one of the them is isosceles, the other has to be an isosceles or an equilateral triangle. We can easily arrive at the answer if that is the case.


In the above case 2OBD = BDA
We also have OBD+DBO= BDA
therefore OBD=DBO and so triangle OBD is equilateral from which we can find BAD=BAO=30 degrees
_________________

Srinivasan Vaidyaraman
Sravna Holistic Solutions
http://www.sravnatestprep.com

Holistic and Systematic Approach

Intern
Intern
avatar
Joined: 18 Sep 2013
Posts: 5
WE: Engineering (Manufacturing)
As shown in the figure above, line segments AB and AC are ta  [#permalink]

Show Tags

New post 25 Aug 2015, 02:59
honchos wrote:
Attachment:
geometry_graphics_1.gif
As shown in the figure above, line segments AB and AC are tangent to circle O. If line segments BD and DA have the same length, what is angle BAO? (Note: Figure not drawn to scale.)

A. 15º
B. 30º
C. 36º
D. 45º
E. 50º


Angle OBA = 90

Angle ODB = Angle DBA + Angle DAB ---------- (Exterior angle = Sum of opposite interior angles)

We can say ODB is double the angle DBA as the triangle ADB is isosceles ................. Which In turn means Angle OBD is double the angle DBA As the triangle BOD is isosceles

Considering above Angle OBA = 90 can only be split in 30 + 60 ....... so the angle OAB = 30
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8816
Premium Member
Re: As shown in the figure above, line segments AB and AC are ta  [#permalink]

Show Tags

New post 26 Oct 2018, 23:33
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 Bot
Re: As shown in the figure above, line segments AB and AC are ta &nbs [#permalink] 26 Oct 2018, 23:33
Display posts from previous: Sort by

As shown in the figure above, line segments AB and AC are ta

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.