GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 11 Jul 2020, 14:04

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

In the figure shown, AC = 2 and BD = DC = 1. What is the measure of

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

Hide Tags

Find Similar Topics 
Director
Director
User avatar
B
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 515
Location: Bangladesh
Concentration: Finance, Leadership
GPA: 2.81
WE: Business Development (Real Estate)
In the figure shown, AC = 2 and BD = DC = 1. What is the measure of  [#permalink]

Show Tags

New post Updated on: 17 Jun 2017, 13:07
4
Top Contributor
28
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

91% (01:50) correct 9% (02:22) wrong based on 1399 sessions

HideShow timer Statistics

Attachment:
2018.OG.05.026.q.png
2018.OG.05.026.q.png [ 32.11 KiB | Viewed 17607 times ]

In the figure shown, AC = 2 and BD = DC = 1. What is the measure of angle ABD?

A. 15°
B. 20°
C. 30°
D. 40°
E. 45°

Originally posted by AbdurRakib on 17 Jun 2017, 10:21.
Last edited by Bunuel on 17 Jun 2017, 13:07, edited 1 time in total.
Renamed the topic and edited the question.
Most Helpful Expert Reply
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 11 Sep 2015
Posts: 4959
Location: Canada
GMAT 1: 770 Q49 V46
In the figure shown, AC = 2 and BD = DC = 1. What is the measure of  [#permalink]

Show Tags

New post Updated on: 16 Apr 2018, 11:40
10
Top Contributor
2
AbdurRakib wrote:
Attachment:
2018.OG.05.026.q.png

In the figure shown, AC = 2 and BD = DC = 1. What is the measure of angle ABD?

A. 15°
B. 20°
C. 30°
D. 40°
E. 45°


If AC = 2 and DC = 1, then we can conclude that AD = 1
Add this information to the diagram...
Image

If AD = 1 and BD = 1, then ∆ABD is an ISOSCELES triangle, which means ∠DAB = ∠ABD are EQUAL...
Image

If we let x = BOTH ∠DAB and ∠ABD, then we can use the fact that angles in a triangle add to 180º
We can write: x + x + 120 = 180
Simplify: 2x + 120 = 180
Solve: x = 30

In other words, ∠ABD = 30º

Answer: C

RELATED VIDEOS



_________________
Test confidently with gmatprepnow.com
Image

Originally posted by BrentGMATPrepNow on 03 Jul 2017, 11:14.
Last edited by BrentGMATPrepNow on 16 Apr 2018, 11:40, edited 1 time in total.
General Discussion
Director
Director
User avatar
V
Joined: 04 Dec 2015
Posts: 723
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
GMAT ToolKit User
Re: In the figure shown, AC = 2 and BD = DC = 1. What is the measure of  [#permalink]

Show Tags

New post 17 Jun 2017, 10:27
1
AbdurRakib wrote:
Attachment:
2018.OG.05.026.q.png
A. 15°
B. 20°
C. 30°
D. 40°
E. 45°


Given BD = DC = 1

AC = 2.

AC = AD + DC => 2 = AD - 1

Therefore AD = 1

\(\triangle\) ABD and \(\triangle\) BDC are isosceles triangles.

\(\triangle\) ABD is isosceles, sides AD = BD = 1. Therefore \(\angle\) BAD = \(\angle\) ABD. Let this angle be x.

Given \(\angle\) ADB is \(120^{\circ}\)

\(\angle\) ADB + \(\angle\) BAD + \(\angle\) ABD = 180

\(120 + x + x = 180\)

\(2x = 180 - 120 = 60\)

\(x = \frac{60}{2} = 30^{\circ}\). Answer (C)...
Manager
Manager
User avatar
S
Joined: 23 May 2017
Posts: 225
Concentration: Finance, Accounting
WE: Programming (Energy and Utilities)
Re: In the figure shown, AC = 2 and BD = DC = 1. What is the measure of  [#permalink]

Show Tags

New post 03 Jul 2017, 11:22
2
Attachment:
FullSizeRender (6).jpg
FullSizeRender (6).jpg [ 44.9 KiB | Viewed 16961 times ]


+ 30
Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3249
Location: India
GPA: 3.12
Re: In the figure shown, AC = 2 and BD = DC = 1. What is the measure of  [#permalink]

Show Tags

New post 04 Jul 2017, 01:55
Angle BDC is 60 degree(because the angle in a straight line is equal to 180 degree)
Since BD = DC(as given in the question stem) the triangle must be equilateral.
Therefere DC=1.

Since AC=2, AD = AC - DC = 1
Angle ABD = Angle DAB = x(Angles opposite equal sides are equal)


We know that the sum of angles in a triangle is 180 degree,
2x + 120 = 180
Angle ABD(x) = 30 degree(Option C)
_________________
You've got what it takes, but it will take everything you've got
Manager
Manager
User avatar
G
Joined: 22 Nov 2016
Posts: 245
Concentration: Leadership, Strategy
Reviews Badge
Re: In the figure shown, AC = 2 and BD = DC = 1. What is the measure of  [#permalink]

Show Tags

New post 04 Jul 2017, 09:22
1
AC-DC=AD
AD = 1, this makes triangle ADC an isosceles triangle

Sum of interior opposite angles = exterior angle.
\(\angle BAD + \angle ABD = \angle BDC\)
Here these two angles are equal, lets say x.

Since AC is a straight line, \(\angle BDC = 180^ {\circ} - 120^ {\circ} = 60^ {\circ}\)

Hence \(\angle BAD + \angle ABD = 60^ {\circ}\)
x+x=60
x=30

Answer is C
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11083
Location: United States (CA)
Re: In the figure shown, AC = 2 and BD = DC = 1. What is the measure of  [#permalink]

Show Tags

New post 15 Nov 2017, 15:46
AbdurRakib wrote:
Attachment:
2018.OG.05.026.q.png

In the figure shown, AC = 2 and BD = DC = 1. What is the measure of angle ABD?

A. 15°
B. 20°
C. 30°
D. 40°
E. 45°


Since AC = 2 and DC = 1, AD must be 1. Since BD = 1, this makes triangle ABD an isosceles triangle with angle D as the vertex angle and angles A and ABD as the base angles. We know that angles A and ABD are equal because the sides opposite them are equal. If we let each of the base angles = x, we can create the following equation:

x + x + 120 = 180

2x = 60

x = 30

Answer: C
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

  214 REVIEWS

5-STARS RATED ONLINE GMAT QUANT SELF STUDY COURSE

NOW WITH GMAT VERBAL (BETA)

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Manager
Manager
avatar
S
Joined: 23 Jul 2019
Posts: 173
GPA: 3.9
In the figure shown, AC = 2 and BD = DC = 1. What is the measure of  [#permalink]

Show Tags

New post 27 Sep 2019, 07:16
Can someone help me, I have a flaw in my logic.
I totally understand it, but I would have solved it from the second triangle.

Is it true that angles in the triangle on the right are 60 degree?

I somehow got stuck because I thought that if those angles are 60, the upper angle (aka the one we are looking for) has to be 120.
Is this wrong because it would only be 120 if I would draw a line from up there and the touch on the line would make it 180?

See drawing:
Attachments

aaa.PNG
aaa.PNG [ 249.06 KiB | Viewed 4758 times ]


_________________
Let's get some
Manager
Manager
User avatar
S
Joined: 12 Dec 2016
Posts: 79
Re: In the figure shown, AC = 2 and BD = DC = 1. What is the measure of  [#permalink]

Show Tags

New post 18 Jun 2020, 23:24
chrtpmdr wrote:
Can someone help me, I have a flaw in my logic.
I totally understand it, but I would have solved it from the second triangle.

Is it true that angles in the triangle on the right are 60 degree?

I somehow got stuck because I thought that if those angles are 60, the upper angle (aka the one we are looking for) has to be 120.
Is this wrong because it would only be 120 if I would draw a line from up there and the touch on the line would make it 180?

See drawing:



Are you saying angle ABC is 120 as well? That's where the error is. You can solve this many ways: the easy way is to realize that angle BDC is 60(linear pair). AC= 2 (given).If DC=1, then AD= 1 (AD+DB=AC). That means triangle ADB is an isosceles triangle with base angles DAB and DBA congruent. angle DAB + angle DBA+120=180. From there you get angle DBA is equal to 30 degrees.

Now if you wanted to use the triangle on the right, you have correctly deduced that the triangle on the right is equiangular. Note that segment BD is the median of triangle ABC. Since AD=BD=DC, we know that the triangle ABC is a right triangle. (the median on the hypotenuse of a right triangle divides the triangle into two isosceles triangles. That means ABC is a right angle. Since DBC is 60 degrees, then ABD is 30 degrees.
GMAT Club Bot
Re: In the figure shown, AC = 2 and BD = DC = 1. What is the measure of   [#permalink] 18 Jun 2020, 23:24

In the figure shown, AC = 2 and BD = DC = 1. What is the measure of

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne