It is currently 22 Feb 2018, 18:25

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# M21-03

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43867

### Show Tags

16 Sep 2014, 00:10
Expert's post
4
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

55% (01:20) correct 45% (01:17) wrong based on 121 sessions

### HideShow timer Statistics

If in triangle $$ABC$$ point $$D$$ lies on side $$AC$$, what is the value of $$\angle BCA$$ ?

(1) The value of $$\angle ABD$$ is half that of $$\angle BDC$$

(2) The value of $$\angle DBC$$ is 10 degrees
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 43867

### Show Tags

16 Sep 2014, 00:10
Expert's post
1
This post was
BOOKMARKED
Official Solution:

Statements (1) and (2) combined are insufficient. Let $$\angle ABD$$ be $$x$$. Then, $$\angle BDA = 180 - 2x$$ and $$\angle BAC = x$$. The sum of the angles of triangle ABC must equal 180. So, $$\angle BCA + \angle ABC + \angle BAC = \angle BCA + (x + 10) + (x) = 180$$. Without knowing $$x$$ we cannot find $$\angle BCA$$.

_________________
Intern
Joined: 01 Apr 2015
Posts: 3

### Show Tags

25 Jul 2016, 08:20
how did you determine that angle ABD = angle BAC ?
Intern
Joined: 31 Jan 2016
Posts: 24
Concentration: Finance, Statistics
GMAT 1: 690 Q47 V37
GPA: 3.6

### Show Tags

05 Sep 2016, 20:59
aramesh19 wrote:
how did you determine that angle ABD = angle BAC ?

Because Angle BDC is an exterior angle to Angle BAC and Angle ABD

An exterior angle of a triangle is equal to the sum of the opposite interior angles

http://www.mathopenref.com/triangleextangletheorem.html
http://www.mathopenref.com/triangleextangle.html
_________________

If you like my post, please send some kudos! :D

Intern
Joined: 17 Aug 2016
Posts: 49

### Show Tags

25 Jan 2017, 11:07
why it is not C? Isn't BAC = 180 - 2x - 10?
Math Expert
Joined: 02 Sep 2009
Posts: 43867

### Show Tags

26 Jan 2017, 06:06
bazu wrote:
why it is not C? Isn't BAC = 180 - 2x - 10?

When a DS question asks about the value of some variable, then the statement(s) is sufficient ONLY if you can get the single numerical value of this variable. Without knowing x we cannot get the measure of angle BAC.
_________________
Senior Manager
Joined: 08 Jun 2015
Posts: 369
Location: India
GMAT 1: 640 Q48 V29

### Show Tags

07 Nov 2017, 04:36
The key here is that all DS questions need a definite answer. Solve for both the conditions one by one. Solve and you will get the answer as option E.
_________________

" The few , the fearless "

Intern
Joined: 09 Nov 2017
Posts: 3

### Show Tags

09 Nov 2017, 09:07
spetznaz wrote:
The key here is that all DS questions need a definite answer. Solve for both the conditions one by one. Solve and you will get the answer as option E.

There is no options for Math question, at least they are not published.
Intern
Joined: 09 Nov 2017
Posts: 3

### Show Tags

09 Nov 2017, 09:31
Bunuel wrote:
Official Solution:

Statements (1) and (2) combined are insufficient. Let $$\angle ABD$$ be $$x$$. Then, $$\angle BDA = 180 - 2x$$ and $$\angle BAC = x$$. The sum of the angles of triangle ABC must equal 180. So, $$\angle BCA + \angle ABC + \angle BAC = \angle BCA + (x + 10) + (x) = 180$$. Without knowing $$x$$ we cannot find $$\angle BCA$$.

What the hell is answer E? Here is the solution:
(1) triangle ABD: $$\angle ABD + \angle BDA + \angle DAB = (x) + (180 - 2x) + (y) = 180$$. From it we get $$x = y (\angle ABD = \angle DAB$$) or $$4x = 180$$
(2) Using where you ended up $$\angle BCA + \angle ABC + \angle BAC = \angle BCA + (x + 10) + (x) = 180$$ we get:
Correct Answer - 80 - (click and drag your mouse to see the answer)
Math Expert
Joined: 02 Sep 2009
Posts: 43867

### Show Tags

09 Nov 2017, 09:45
olexi wrote:
Bunuel wrote:
Official Solution:

Statements (1) and (2) combined are insufficient. Let $$\angle ABD$$ be $$x$$. Then, $$\angle BDA = 180 - 2x$$ and $$\angle BAC = x$$. The sum of the angles of triangle ABC must equal 180. So, $$\angle BCA + \angle ABC + \angle BAC = \angle BCA + (x + 10) + (x) = 180$$. Without knowing $$x$$ we cannot find $$\angle BCA$$.

What the hell is answer E? Here is the solution:
(1) triangle ABD: $$\angle ABD + \angle BDA + \angle DAB = (x) + (180 - 2x) + (y) = 180$$.From it we get $$x = y (\angle ABD = \angle DAB$$) or $$4x = 180$$.
(2) Using where you ended up $$\angle BCA + \angle ABC + \angle BAC = \angle BCA + (x + 10) + (x) = 180$$ we get:
Correct Answer - 80 - (click and drag your mouse to see the answer)

You are wrong. The correct answer is E. The highlighted part is not correct. From (x) + (180 - 2x) + (x) = 180 you don't get 4x = 180.
_________________
Intern
Joined: 09 Nov 2017
Posts: 3

### Show Tags

16 Nov 2017, 11:49
Bunuel wrote:
You are wrong. The correct answer is E. The highlighted part is not correct. From (x) + (180 - 2x) + (x) = 180 you don't get 4x = 180.

You are right, but I'm still not sure what answer E means.
Math Expert
Joined: 02 Sep 2009
Posts: 43867

### Show Tags

16 Nov 2017, 19:40
olexi wrote:
Bunuel wrote:
You are wrong. The correct answer is E. The highlighted part is not correct. From (x) + (180 - 2x) + (x) = 180 you don't get 4x = 180.

You are right, but I'm still not sure what answer E means.

E means that Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

For this particular question it means that the measure of angle BCA cannot be determined, different values of x give different value of angle BCA.
_________________
Re: M21-03   [#permalink] 16 Nov 2017, 19:40
Display posts from previous: Sort by

# M21-03

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

Moderators: chetan2u, Bunuel

 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®.