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

 It is currently 22 Oct 2019, 15:41 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

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.  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

Director  B
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 524
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

3
Top Contributor
20 00:00

Difficulty:   5% (low)

Question Stats: 91% (01:50) correct 9% (02:23) wrong based on 1121 sessions

HideShow timer Statistics

Attachment: 2018.OG.05.026.q.png [ 32.11 KiB | Viewed 13497 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°

_________________
Md. Abdur Rakib

Please Press +1 Kudos,If it helps
Sentence Correction-Collection of Ron Purewal's "elliptical construction/analogies" for SC Challenges

Originally posted by AbdurRakib on 17 Jun 2017, 11:21.
Last edited by Bunuel on 17 Jun 2017, 14:07, edited 1 time in total.
Renamed the topic and edited the question.
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4018
In the figure shown, AC = 2 and BD = DC = 1. What is the measure of  [#permalink]

Show Tags

8
Top Contributor
1
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... If AD = 1 and BD = 1, then ∆ABD is an ISOSCELES triangle, which means ∠DAB = ∠ABD are EQUAL... 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

RELATED VIDEOS

_________________

Originally posted by GMATPrepNow on 03 Jul 2017, 12:14.
Last edited by GMATPrepNow on 16 Apr 2018, 12:40, edited 1 time in total.
General Discussion
Director  V
Joined: 04 Dec 2015
Posts: 743
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
Re: In the figure shown, AC = 2 and BD = DC = 1. What is the measure of  [#permalink]

Show Tags

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  S
Joined: 23 May 2017
Posts: 234
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

2
Attachment: FullSizeRender (6).jpg [ 44.9 KiB | Viewed 12877 times ]

+ 30
_________________
If you like the post, please award me Kudos!! It motivates me
Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3333
Location: India
GPA: 3.12
Re: In the figure shown, AC = 2 and BD = DC = 1. What is the measure of  [#permalink]

Show Tags

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  S
Joined: 22 Nov 2016
Posts: 202
Location: United States
GPA: 3.4
Re: In the figure shown, AC = 2 and BD = DC = 1. What is the measure of  [#permalink]

Show Tags

1
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

_________________
Kudosity killed the cat but your kudos can save it.
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8129
Location: United States (CA)
Re: In the figure shown, AC = 2 and BD = DC = 1. What is the measure of  [#permalink]

Show Tags

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

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

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

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager  B
Joined: 24 Jul 2019
Posts: 73
In the figure shown, AC = 2 and BD = DC = 1. What is the measure of  [#permalink]

Show Tags

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 [ 249.06 KiB | Viewed 701 times ]

_________________
Don't wait for the opportunity to knock.
Go kick in the door. In the figure shown, AC = 2 and BD = DC = 1. What is the measure of   [#permalink] 27 Sep 2019, 08:16
Display posts from previous: Sort by

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  