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

It is currently 19 Nov 2019, 06:48

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, point D divides side BC of triangle ABC into segments

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

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 03 Jan 2016
Posts: 3
Re: In the figure, point D divides side BC of triangle ABC into segments  [#permalink]

Show Tags

New post 11 Aug 2016, 16:19
here are my way to solve it:
Attachments

mi-proceso.png
mi-proceso.png [ 40.48 KiB | Viewed 7476 times ]

Intern
Intern
avatar
Joined: 03 Jan 2016
Posts: 3
Re: In the figure, point D divides side BC of triangle ABC into segments  [#permalink]

Show Tags

New post 12 Aug 2016, 21:28
1
A GMAT way to answer the problem, the best way I can explain it. (click on the image and then in the "magnifying glass" at the top left to enlarge to full size)
Don't forget +1KUDOS !!!
Attachments

triangle-problem.png
triangle-problem.png [ 85.25 KiB | Viewed 7010 times ]

Senior Manager
Senior Manager
User avatar
G
Joined: 19 Oct 2012
Posts: 256
Location: India
Concentration: General Management, Operations
GMAT 1: 660 Q47 V35
GMAT 2: 710 Q50 V38
GPA: 3.81
WE: Information Technology (Computer Software)
Re: In the figure, point D divides side BC of triangle ABC into segments  [#permalink]

Show Tags

New post 23 Aug 2016, 22:54
vigrah wrote:
say angle CAB=y
since sum of angles in a triangleis 180\
x+y+45=180
x+y=135 equation 1

line AD is dividing BC in 2:1 ratio
hence
X+2/3Y+60=180
X+2/3y=120 equation 2
solving equation 1 &2 we get x=75
answer is D



This DOES NOT give us the correct solution. There is a calculation mistake here. Using the calculation mentioned, we get x=90 which is incorrect. This basically implies that the statement
"line AD is dividing BC in 2:1 ratio - > therefore corresponding angles also get divided in the same proportion" is invalid. The only way to go forward is to follow the approach that Bunuel mentioned.

Hope this helps clear the confusion around this.

Thanks.
_________________
Citius, Altius, Fortius
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: In the figure, point D divides side BC of triangle ABC into segments  [#permalink]

Show Tags

New post 12 Nov 2016, 20:57
enigma123 wrote:
Image
In the figure, point D divides side BC of triangle ABC into segments BD and DC of lengths 1 and 2 units respectively. Given that ÐADC = 60º and ÐABD = 45º, what is the measure of angle x in degrees? (Note:
Figure is not drawn to scale.)

A. 55
B. 60
C. 70
D. 75
E. 90

Any idea guys what will be the correct answer please? Also any idea how can I cut and paste the pictures in my post? Is it possible?

Attachment:
The attachment Triangle.png is no longer available


Answer: Option D

Please check solution
Attachments

File comment: www.GMATinsight.com
12.jpg
12.jpg [ 110.35 KiB | Viewed 2484 times ]


_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Intern
Intern
avatar
Joined: 28 Sep 2017
Posts: 2
Re: In the figure, point D divides side BC of triangle ABC into segments  [#permalink]

Show Tags

New post 06 Dec 2017, 20:10
1
Hi bunuel,

Sorry for bumping. A quick question.

How do we know that AD is not equal to 1. If it is equal to 1 then the ratio 2:1 when a perpendicular is drawn does not hold good right? Am i missing something?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59147
Re: In the figure, point D divides side BC of triangle ABC into segments  [#permalink]

Show Tags

New post 06 Dec 2017, 20:40
gauthamvm wrote:
Hi bunuel,

Sorry for bumping. A quick question.

How do we know that AD is not equal to 1. If it is equal to 1 then the ratio 2:1 when a perpendicular is drawn does not hold good right? Am i missing something?


Image

x=45+30=75.

Notes:
Sides with one blue segment crossing them are equal and sides with two blues segments crossing them are equal too.

CO is perpendicular to AD --> OD=1 (from 30-60-90 right triangle property as sides are in ratio \(1:\sqrt{3}:2\)) --> as OD=BD=1 then ODB is an isosceles triangle.
_________________
Senior Manager
Senior Manager
avatar
P
Joined: 09 Jun 2014
Posts: 351
Location: India
Concentration: General Management, Operations
Reviews Badge
Re: In the figure, point D divides side BC of triangle ABC into segments  [#permalink]

Show Tags

New post 20 Aug 2019, 21:03
vigrah wrote:
say angle CAB=y
since sum of angles in a triangle is 180
x+y+45=180
x+y=135 equation 1

line AD is dividing BC in 2:1 ratio
hence
X+2/3Y+60=180
X+2/3y=120 equation 2
solving equation 1 &2 we get x=75
answer is D


Bunnel/Experts,

I have a doubt here.I understand angles and sides ratio will be proportional.

So If I see angle opposite to side with lenght 1 is 15 degree .So why not we
directly comprehend angle opposite to CB(3 units) is 45 degrees.

from this I will get angle y as 45 degrees
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59147
Re: In the figure, point D divides side BC of triangle ABC into segments  [#permalink]

Show Tags

New post 20 Aug 2019, 22:00
prabsahi wrote:
vigrah wrote:
say angle CAB=y
since sum of angles in a triangle is 180
x+y+45=180
x+y=135 equation 1

line AD is dividing BC in 2:1 ratio
hence
X+2/3Y+60=180
X+2/3y=120 equation 2
solving equation 1 &2 we get x=75
answer is D


Bunnel/Experts,

I have a doubt here.I understand angles and sides ratio will be proportional.

So If I see angle opposite to side with lenght 1 is 15 degree .So why not we
directly comprehend angle opposite to CB(3 units) is 45 degrees.

from this I will get angle y as 45 degrees


The solution you are quoting is not correct. Please check the discussion on previous pages.
_________________
Manager
Manager
User avatar
S
Joined: 18 Jul 2015
Posts: 82
GMAT 1: 530 Q43 V20
WE: Analyst (Consumer Products)
GMAT ToolKit User
In the figure, point D divides side BC of triangle ABC into segments  [#permalink]

Show Tags

New post 13 Oct 2019, 09:33
Bunuel wrote:
enigma123 wrote:
Image

In the figure, point D divides side BC of triangle ABC into segments BD and DC of lengths 1 and 2 units respectively. Given that ÐADC = 60º and ÐABD = 45º, what is the measure of angle x in degrees? (Note:
Figure is not drawn to scale.)

(A) 55
(B) 60
(C) 70
(D) 75
(E) 90

Any idea guys what will be the correct answer please? Also any idea how can I cut and paste the pictures in my post? Is it possible?


Complete solution for all the angles is in the image below:

Image

x=45+30=75.

Notes:
Sides with one blue segment crossing them are equal and sides with two blues segments crossing them are equal too.

CO is perpendicular to AD --> OD=1 (from 30-60-90 right triangle property as sides are in ratio \(1:\sqrt{3}:2\)) --> as OD=BD=1 then ODB is an isosceles triangle.

<CDO and <BDO are supplementary to each other (supplementary angles are two angles that add up to 180°), so <BDO=120 --> <DAB=180-(120+45)=15.

As ODB is an isosceles triangle --> <DOB=<DBO=30. <OBA=45-30=15 --> AOB is an isosceles triangle, so OA=OB. Also COB is an isosceles triangle, so CO=OB --> OA=CO=OB. So, AOC is an isosceles triangle --> <CAO=<OCA=45 (as <COA=90) --> x=45+30=75.

Answer: D.

P.S. You can attach image files directly to the post.

Attachment:
Triangle complete.PNG


Hi Bunuel,

I have two questions which came in when I was solving the problem. Tried reading through the other explanations but am still unclear.

1. When you drew the segment OB, how did you determine that it will split angle B (i.e. 45) into 30 and 15? Why could it not be any other split like 20 and 25 or 10 and 35 etc?
2. In triangle AOC we know that angle O is 90, but then how did you conclude that the other 2 angles are 45 each and not any other split?

Warm Regards,
Pritishd
_________________
Cheers. Wishing Luck to Every GMAT Aspirant!
GMAT Club Bot
In the figure, point D divides side BC of triangle ABC into segments   [#permalink] 13 Oct 2019, 09:33

Go to page   Previous    1   2   [ 29 posts ] 

Display posts from previous: Sort by

In the figure, point D divides side BC of triangle ABC into segments

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





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