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

 It is currently 20 Oct 2019, 04:44 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, 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

CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: In the figure, point D divides side BC of triangle ABC into segments  [#permalink]

Show Tags

enigma123 wrote: 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

Attachments

File comment: www.GMATinsight.com 12.jpg [ 110.35 KiB | Viewed 2406 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
Senior Manager  P
Joined: 29 Jun 2017
Posts: 424
GPA: 4
WE: Engineering (Transportation)
Re: In the figure, point D divides side BC of triangle ABC into segments  [#permalink]

Show Tags

2
Attachment: IMG_6850.JPG [ 1.67 MiB | Viewed 2239 times ]
. see attached pic

Answer is 75 degrees.
_________________
Give Kudos for correct answer and/or if you like the solution.
Intern  Joined: 28 Sep 2017
Posts: 2
Re: In the figure, point D divides side BC of triangle ABC into segments  [#permalink]

Show Tags

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 V
Joined: 02 Sep 2009
Posts: 58434
Re: In the figure, point D divides side BC of triangle ABC into segments  [#permalink]

Show Tags

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? 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.
_________________
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4009
Re: In the figure, point D divides side BC of triangle ABC into segments  [#permalink]

Show Tags

3
Top Contributor
1
enigma123 wrote: 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

Attachment:
Triangle.png

Attachment:

First let's add a line from point C so that it is PERPENDICULAR to line AD
Also, note that, ∠EDB is 120° since it lies on a line with a 60° angle. Since we already know 2 angles in ∆CED, we can see that the remaining angle, ∠ECD, is 30°, which means ∆CED is a 30-60-90 right triangle.
So, ∆CED is a 30-60-90 right triangle AND we know that the hypotenuse CD has length 2, we can conclude that side ED has length 1. Now draw a line from E to B.
Since ED = EB (both have length 1), we can see that ∆EDB is an ISOSCELES TRIANGLE, which means the two remaining angles are each 30° Next, ∠EAB is 150° since it shares a line with a 30° angle
Also, since we were originally told that ∠CBA is 45°, we can conclude that ∠ABE is 15° Now focus on ∆CBE
Notice that this triangle is an ISOSCELES triangle, because ∠ECB = ∠EBC = 30°
This means that side EC = side EB Now focus on ∆EAB
Since we already know two of the angles in this triangle (150° and 15°), we can conclude that = ∠EAB = 15° Stay focused on ∆EAB
This triangle is an ISOSCELES triangle, because ∠EAB = ∠EBA = 15°
This means that side AE = side EB Now focus on ∆ACE
Since CE = EA, this is an ISOSCELES triangle
Since one angle = 90°, the other two angles are each 45° At this point, we can see that x = 45° + 30° = 75°

Cheers,
Brent
_________________
Intern  B
Joined: 18 May 2016
Posts: 34
Re: In the figure, point D divides side BC of triangle ABC into segments  [#permalink]

Show Tags

1
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

This answer is wrong. Solving this system does not yield x=75, but x=90, and y=45.
This answer should not have so many kudos, it is very misleading.
Senior Manager  P
Joined: 09 Jun 2014
Posts: 352
Location: India
Concentration: General Management, Operations
Re: In the figure, point D divides side BC of triangle ABC into segments  [#permalink]

Show Tags

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

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 V
Joined: 02 Sep 2009
Posts: 58434
Re: In the figure, point D divides side BC of triangle ABC into segments  [#permalink]

Show Tags

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

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  S
Joined: 18 Jul 2015
Posts: 72
GMAT 1: 530 Q43 V20 WE: Analyst (Consumer Products)
In the figure, point D divides side BC of triangle ABC into segments  [#permalink]

Show Tags

Bunuel wrote:
enigma123 wrote: 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: 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.

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! 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  