Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack
GMAT Club

 It is currently 24 Mar 2017, 15:24

### 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

# If angle ABC is 30 degrees, what is the area of triangle BCE?

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 08 Nov 2010
Posts: 415
Followers: 7

Kudos [?]: 110 [0], given: 161

If angle ABC is 30 degrees, what is the area of triangle BCE? [#permalink]

### Show Tags

27 Aug 2011, 10:19
3
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

43% (02:53) correct 57% (02:27) wrong based on 111 sessions

### HideShow timer Statistics

If angle ABC is 30 degrees, what is the area of triangle BCE?

(1) Angle CDF is 120 degrees, lines L and M are parallel, and AC = 6, BC = 12, and EC = 2AC
(2) Angle DCG is 60 degrees, angle CDG is 30 degrees, angle FDG = 90, and GC = 6, CD = 12 and EC = 12

[Reveal] Spoiler:
Attachment:

DS.gif [ 3.64 KiB | Viewed 1814 times ]
[Reveal] Spoiler: OA

_________________
Senior Manager
Joined: 08 Nov 2010
Posts: 415
Followers: 7

Kudos [?]: 110 [0], given: 161

Re: If angle ABC is 30 degrees, what is the area of triangle BCE? [#permalink]

### Show Tags

27 Aug 2011, 10:23
Not sure how to add this in a hide mode, this is the OA

 # 1. Since EC = 2AC, EA = CA, EC = 2(6) = 12 and line AB is an angle bisector of angle EBC. This means that angle ABC = angle ABE. Since we know that angle ABC = 30, we know that angle ABE = 30. Further, since lines L and M are parallel, we know that line AB is perpendicular to line EC, meaning angle BAC is 90. 2. Since all the interior angles of a triangle must sum to 180: angle ABC + angle BCA + angle BAC = 180 30 + angle BCA + 90 = 180 angle BCA = 60 3. Since all the interior angles of a triangle must sum to 180: angle BCA + angle ABC + angle ABE + angle AEB = 180 60 + 30 + 30 + angle AEB = 180 angle AEB = 60 4. This means that triangle BCA is an equilateral triangle. 5. To find the area of triangle BCE, we need the base (= 12 from above) and the height, i.e., line AB. Since we know BC and AC and triangle ABC is a right triangle, we can use the Pythagorean theorem on triangle ABC to find the length of AB. 62 + (AB)2 = 122 AB2 = 144 - 36 = 108 AB = 1081/2 6. Area = .5bh Area = .5(12)(1081/2) = 6*1081/2 7. Statement (1) is SUFFICIENT# Evaluate Statement (2) alone. 1. The sum of the interior angles of any triangle must be 180 degrees. DCG + GDC + CGD = 180 60 + 30 + CGD = 180 CGD = 90 Triangle CGD is a right triangle. 2. Using the Pythagorean theorem, DG = 1081/2 (CG)2 + (DG)2 = (CD)2 62 + (DG)2 = 122 DG = 1081/2 3. At this point, it may be tempting to use DG = 1081/2 as the height of the triangle BCE, assuming that lines AB and DG are parallel and therefore AB = 1081/2 is the height of triangle BCE. However, we must show two things before we can use AB = 1081/2 as the height of triangle BCE: (1) lines L and M are parallel and (2) AB is the height of triangle BCE (i.e., angle BAC is 90 degrees). 4. Lines L and M must be parallel since angles FDG and CGD are equal and these two angles are alternate interior angles formed by cutting two lines with a transversal. If two alternate interior angles are equal, we know that the two lines that form the angles (lines L and M) when cut by a transversal (line DG) must be parallel. 5. Since lines L and M are parallel, DG = the height of triangle BCE = 1081/2. Note that it is not essential to know whether AB is the height of triangle BCE. It is sufficient to know that the height is 1081/2. To reiterate, we know that the height is 8 since the height of BCE is parallel to line DG, which is 1081/2. 6. Since we know both the height (1081/2) and the base (CE = 12) of triangle BCE, we know that the area is: .5*12*1081/2 = 6*1081/2 7. Statement (2) alone is SUFFICIENT.# Since Statement (1) alone is SUFFICIENT and Statement (2) alone is SUFFICIENT, answer D is correct.

_________________
Intern
Status: Juggling Kid, wife, 2 bosses, and 15 clients
Joined: 13 May 2011
Posts: 15
Location: Jacksonville, FL
Schools: H W S
WE 1: 2 years IT
WE 2: 7 years IT Management
Followers: 0

Kudos [?]: 5 [0], given: 6

Re: If angle ABC is 30 degrees, what is the area of triangle BCE? [#permalink]

### Show Tags

27 Aug 2011, 21:49
I see more assumptions than statements in the following part

and line AB is an angle bisector of angle EBC. This means that angle ABC = angle ABE. Since we know that angle ABC = 30, we know that angle ABE = 30. Further, since lines L and M are parallel, we know that line AB is perpendicular to line EC, meaning angle BAC is 90.
_________________

MGMAT1 Q48 V35 680
PR1 Q44 V37 660
PR2 Q51 V31 660
PR3 Q51 V37 710
PR4 Q50 V37 700
PR5 Q51 V41 730
MGMAT2 Q49 V45 760
GMATPREP1 Q49 V43 730
GMATPREP2 Q49 V43 730
MGMAT3 Q51 V36 710
GMATPREP1 Q51 V34 690

Senior Manager
Joined: 08 Nov 2010
Posts: 415
Followers: 7

Kudos [?]: 110 [0], given: 161

Re: If angle ABC is 30 degrees, what is the area of triangle BCE? [#permalink]

### Show Tags

27 Aug 2011, 23:20
DeepGagan wrote:
I see more assumptions than statements in the following part

and line AB is an angle bisector of angle EBC. This means that angle ABC = angle ABE. Since we know that angle ABC = 30, we know that angle ABE = 30. Further, since lines L and M are parallel, we know that line AB is perpendicular to line EC, meaning angle BAC is 90.

Agreed. Point B can easily be shifted to the left and still comply with all the data, but the angle will not be 90.
_________________
Current Student
Joined: 24 Feb 2014
Posts: 47
Concentration: Finance, Marketing
GMAT 1: 710 Q49 V38
GPA: 3.8
WE: Information Technology (Telecommunications)
Followers: 1

Kudos [?]: 9 [0], given: 27

Re: If angle ABC is 30 degrees, what is the area of triangle BCE? [#permalink]

### Show Tags

14 Jun 2014, 12:13
2
This post was
BOOKMARKED
Attachment:

DS.gif [ 3.64 KiB | Viewed 2443 times ]
If angle ABC is 30 degrees, what is the area of triangle BCE?

(1) Angle CDF is 120 degrees, lines L and M are parallel, and AC = 6, BC = 12, and EC = 2AC
(2) Angle DCG is 60 degrees, angle CDG is 30 degrees, angle FDG = 90, and GC = 6, CD = 12 and EC = 12

Last edited by Bunuel on 14 Jun 2014, 12:34, edited 2 times in total.
Renamed the topic and edited the question.
Intern
Joined: 08 Sep 2014
Posts: 18
Followers: 0

Kudos [?]: 16 [0], given: 7

Re: If angle ABC is 30 degrees, what is the area of triangle BCE? [#permalink]

### Show Tags

20 Mar 2015, 17:58
gaurav245 wrote:
Attachment:
DS.gif
If angle ABC is 30 degrees, what is the area of triangle BCE?

(1) Angle CDF is 120 degrees, lines L and M are parallel, and AC = 6, BC = 12, and EC = 2AC
(2) Angle DCG is 60 degrees, angle CDG is 30 degrees, angle FDG = 90, and GC = 6, CD = 12 and EC = 12

The answer I am getting does not match the OA. Please let me know what I am doing wrong. Here's my approach to this problem.

From Stem, angle ABC = 30º

From (1), AC = 6 & BC = 12

Using Law of Sines, sin 30º/AC = sin BAC/BC
So, Sin BAC = 1 => angle BAC = 90º => AB is the altitude and by applying pythagorean theorem, we have, AB = $$6\sqrt{3}$$.
Since, we have AB and EC, it is possible to find area of triangle BCE. Thus, this is SUFFICIENT.

From (2), angle FDG = 90º,
GC = 6, CD = 12, angle DCG = 60º and angle CDG = 30º. Thus, triangle CDG is a right triangle with angle DGC = 90º.
Hence, we can conclude that L || M.

EC = 12, however, we can't assume that AB is perpendicular to EC, nor can we prove this based on the information provided. Hence, this information is INSUFFICIENT.

Therefore, answer (according to me) is A.
Current Student
Status: Birds fly because they have wings, not because they have sky.
Joined: 21 Sep 2014
Posts: 217
Location: Singapore
Concentration: Strategy, Technology
GMAT 1: 740 Q50 V40
GPA: 3.65
WE: Information Technology (Consulting)
Followers: 7

Kudos [?]: 87 [0], given: 73

Re: If angle ABC is 30 degrees, what is the area of triangle BCE? [#permalink]

### Show Tags

20 Mar 2015, 20:41
rdoshi wrote:
gaurav245 wrote:
Attachment:
DS.gif
If angle ABC is 30 degrees, what is the area of triangle BCE?

(1) Angle CDF is 120 degrees, lines L and M are parallel, and AC = 6, BC = 12, and EC = 2AC
(2) Angle DCG is 60 degrees, angle CDG is 30 degrees, angle FDG = 90, and GC = 6, CD = 12 and EC = 12

The answer I am getting does not match the OA. Please let me know what I am doing wrong. Here's my approach to this problem.

From Stem, angle ABC = 30º

From (1), AC = 6 & BC = 12

Using Law of Sines, sin 30º/AC = sin BAC/BC
So, Sin BAC = 1 => angle BAC = 90º => AB is the altitude and by applying pythagorean theorem, we have, AB = $$6\sqrt{3}$$.
Since, we have AB and EC, it is possible to find area of triangle BCE. Thus, this is SUFFICIENT.

From (2), angle FDG = 90º,
GC = 6, CD = 12, angle DCG = 60º and angle CDG = 30º. Thus, triangle CDG is a right triangle with angle DGC = 90º.
Hence, we can conclude that L || M.

EC = 12, however, we can't assume that AB is perpendicular to EC, nor can we prove this based on the information provided. Hence, this information is INSUFFICIENT.

Therefore, answer (according to me) is A.

(2) is sufficient as well. Let me explain.

Area of all the triangles drawn on the same base on one of the parallel lines with third vertex on the other parallel line is same.

You have already figured out that L||M so here it goes.

From the diagram above:

Area of triangle BCE = Area of triangle DCE

Area of triangle DCE = 1/2 * EC * DG

You already know EC and using pythagorean theoram can find DG. Hence, you can get area of triangle DCE and also BCE.
_________________

Regards,
J

--------------------------------------------------
Consider Kudos if I helped in some way!!!

Perseverance is the hard work you do after you get tired of doing the hard work you already did.

Manager
Joined: 03 May 2013
Posts: 76
Followers: 0

Kudos [?]: 10 [0], given: 105

Re: If angle ABC is 30 degrees, what is the area of triangle BCE? [#permalink]

### Show Tags

19 Jun 2015, 20:30
Experts please suggest how AB is Perpendicular to EC ??
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 14395
Followers: 604

Kudos [?]: 174 [0], given: 0

Re: If angle ABC is 30 degrees, what is the area of triangle BCE? [#permalink]

### Show Tags

24 Sep 2016, 09:43
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If angle ABC is 30 degrees, what is the area of triangle BCE?   [#permalink] 24 Sep 2016, 09:43
Similar topics Replies Last post
Similar
Topics:
In triangle ABC, angle A and angle B are 30 and 60 degrees, respective 1 28 Feb 2016, 10:01
9 What is area of triangle ABC? 10 18 Feb 2015, 03:20
6 In triangle ABC, angle ABC is 105 degrees. Is the area of triangle ABC 3 05 Feb 2015, 08:58
5 What is the area of triangle ABC ? 4 21 Feb 2014, 08:12
2 What is the area of the triangle ABC? 4 26 Jul 2012, 05:37
Display posts from previous: Sort by