Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 17 Mar 2010
Posts: 127

If AD is 6 and ADC is a right angle, what is the area of triangular re
[#permalink]
Show Tags
Updated on: 29 Apr 2018, 23:16
Question Stats:
58% (01:45) correct 42% (01:35) wrong based on 542 sessions
HideShow timer Statistics
If AD is 6 and ADC is a right angle, what is the area of triangular region ABC? (1) Angle ABD = 60° (2) AC = 12 Attachment:
Triangle.jpg [ 2.62 KiB  Viewed 21724 times ]
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by amitjash on 17 Sep 2010, 05:03.
Last edited by Bunuel on 29 Apr 2018, 23:16, edited 5 times in total.
Edited the question and added the diagram




Math Expert
Joined: 02 Sep 2009
Posts: 59623

If AD is 6 and ADC is a right angle, what is the area of triangular re
[#permalink]
Show Tags
17 Sep 2010, 05:25
If AD is 6 and ADC is a right angle, what is the area of triangular region ABC?Given: \(AD=6\). Question: \(area_{ABC}=\frac{1}{2}*AD*BC=\frac{1}{2}*6*(BD+DC)=3(BD+DC)=?\) (1) Angle ABD = 60 > triangle ABD is 306090 triangle, so the sides are in ratio \(1:\sqrt{3}:2\) > as AD=6 (larger leg opposite 60 degrees angle) then \(BD=\frac{6}{\sqrt{3}}\) (smallest leg opposite 30 degrees angle). But we still don't know DC. Not sufficient. (2) AC=12, we can find DC. But we still don't know BD. Not sufficient. (1)+(2) We know both BD and DC, hence we can find the area. Sufficient. Answer: C.
_________________




Manager
Joined: 27 Oct 2011
Posts: 116
Location: United States
Concentration: Finance, Strategy
GPA: 3.7
WE: Account Management (Consumer Products)

Re: If AD is 6 and ADC is a right angle, what is the area of triangular re
[#permalink]
Show Tags
15 Apr 2012, 15:11
with statement 1 we can only figure out that the left triangle is a 306090. We cannot just assume that the left triangle is also a 306090. The sides could be longer or shorter than shown. the same idea as statement 1 for 2. no assumptions can be made for the left triangle given that the side is 12. if we combine both questions together then we can find out vital information for both triangles.



Intern
Joined: 26 May 2012
Posts: 6
Concentration: Human Resources, Leadership
GMAT Date: 07042012

Re: If AD is 6 and ADC is a right angle, what is the area of triangular re
[#permalink]
Show Tags
29 Jun 2012, 04:44
but isn't triangle ABD similar to triangle ADC since AD is the perpendicular. so using the ratio of 2:1:√3 we can find all sides of triangle ABD and since AD is common using proportions we can find DC ? and thus the total area ?



Math Expert
Joined: 02 Sep 2009
Posts: 59623

Re: If AD is 6 and ADC is a right angle, what is the area of triangular re
[#permalink]
Show Tags
29 Jun 2012, 05:05
shradhagrover18 wrote: but isn't triangle ABD similar to triangle ADC since AD is the perpendicular. so using the ratio of 2:1:√3 we can find all sides of triangle ABD and since AD is common using proportions we can find DC ? and thus the total area ? No, for (1) we cannot conclude that ABD and ADC are similar. We only know that ABD and ADC are both right triangles (one angle) and share the common side AD (one side), which is not enough to conclude that ABD and ADC are similar. For more check Triangles chapter of Math Book: mathtriangles87197.html
_________________



Manager
Joined: 28 Feb 2011
Posts: 66
Location: India
Concentration: Strategy, Marketing
GPA: 3.77
WE: Analyst (Computer Software)

Re: If AD is 6 and ADC is a right angle, what is the area of triangular re
[#permalink]
Show Tags
10 Jul 2019, 14:15
GittinGud wrote: VeritasKarishma We have no information in the stem to decide whether BC is a straight line. Why are we assuming it is? I am pasting the response that Bunuel posted earlier. Hope that will help in clearing the confusion up. OG13, page 272: A figure accompanying a data sufficiency problem will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2). Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight. You may assume that the positions of points, angles, regions, and so forth exist in the order shown and that angle measures are greater than zero degrees. All figures lie in a plane unless otherwise indicated. OG13, page 150: Figures: A figure accompanying a problem solving question is intended to provide information useful in solving the problem. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.
_________________



Manager
Joined: 07 Feb 2011
Posts: 89

Re: If AD is 6 and ADC is a right angle, what is the area of triangular re
[#permalink]
Show Tags
04 Apr 2013, 11:00
Hey I had the same question as the last poster. How do we know that BD and DC are of the same length? or that angle BAC has been bisected?



Manager
Joined: 26 Sep 2013
Posts: 182
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41

If AD is 6 and ADC is a right angle, what is the area of triangular re
[#permalink]
Show Tags
26 Oct 2013, 11:54
Bunuel wrote: Given: \(AD=6\). Question: \(area_{ABC}=\frac{1}{2}*AD*BC=\frac{1}{2}*6*(BD+DC)=3(BD+DC)=?\) (1) Angle ABD = 60 > triangle ABD is 306090 triangle, so the sides are in ratio \(1:\sqrt{3}:2\) > as AD=6 (larger leg opposite 60 degrees angle) then \(BD=\frac{6}{\sqrt{3}}\) (smallest leg opposite 30 degrees angle). But we still don't know DC. Not sufficient. (2) AC=12, we can find DC. But we still don't know BD. Not sufficient. (1)+(2) We know both BD and DC, hence we can find area. Sufficient. Answer: C. I thought if you dropped something that was perpindicular to the base of a triangle then it was automatically a bisector; so if you found BD using (1) BD MUST equal dc, no?



Manager
Joined: 26 Sep 2013
Posts: 182
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41

If AD is 6 and ADC is a right angle, what is the area of triangular re
[#permalink]
Show Tags
15 Dec 2013, 16:05
Bunuel wrote: Given: \(AD=6\). Question: \(area_{ABC}=\frac{1}{2}*AD*BC=\frac{1}{2}*6*(BD+DC)=3(BD+DC)=?\) (1) Angle ABD = 60 > triangle ABD is 306090 triangle, so the sides are in ratio \(1:\sqrt{3}:2\) > as AD=6 (larger leg opposite 60 degrees angle) then \(BD=\frac{6}{\sqrt{3}}\) (smallest leg opposite 30 degrees angle). But we still don't know DC. Not sufficient. (2) AC=12, we can find DC. But we still don't know BD. Not sufficient. (1)+(2) We know both BD and DC, hence we can find area. Sufficient. Answer: C. I thought if you dropped a line down from a triangle vertex and it formed a right angle on the opposite side then that line bisected the side? So in this case if you know what BD is then you know what DC is?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9859
Location: Pune, India

If AD is 6 and ADC is a right angle, what is the area of triangular re
[#permalink]
Show Tags
15 Dec 2013, 23:21
AccipiterQ wrote: I thought if you dropped a line down from a triangle vertex and it formed a right angle on the opposite side then that line bisected the side? So in this case if you know what BD is then you know what DC is? To figure out whether it holds, why don't you try drawing some extreme figures, say, something like this: Attachment:
Ques3.jpg [ 3.67 KiB  Viewed 8502 times ]
Will this be true in this case? When will it be true? When the triangle is equilateral, sure. Also when the triangle is isosceles if the equal sides form the angle from which the altitude is dropped. Don't put your faith in the figure given. It may be just one of the many possibilities or may be somewhat misleading.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Math Expert
Joined: 02 Sep 2009
Posts: 59623

If AD is 6 and ADC is a right angle, what is the area of triangular re
[#permalink]
Show Tags
07 Feb 2014, 05:27
virendrasd wrote: I think answer is E, since it is not given that BDC points are collinear. That's not correct. OG13, page 272: A figure accompanying a data sufficiency problem will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2). Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight. You may assume that the positions of points, angles, regions, and so forth exist in the order shown and that angle measures are greater than zero degrees. All figures lie in a plane unless otherwise indicated. OG13, page 150: Figures: A figure accompanying a problem solving question is intended to provide information useful in solving the problem. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated. Hope it helps.
_________________



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9859
Location: Pune, India

Re: If AD is 6 and ADC is a right angle, what is the area of triangular re
[#permalink]
Show Tags
12 Jul 2019, 00:05
GittinGud wrote: VeritasKarishma We have no information in the stem to decide whether BC is a straight line. Why are we assuming it is? A figure may not be to scale but lines that look straight are certainly straight. Also, points and angles are in the order in which they are given.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Math Expert
Joined: 02 Sep 2009
Posts: 59623

Re: If AD is 6 and ADC is a right angle, what is the area of triangular re
[#permalink]
Show Tags
04 Apr 2013, 11:25
manimgoindowndown wrote: Hey I had the same question as the last poster. How do we know that BD and DC are of the same length? or that angle BAC has been bisected? They are not equal: \(BD=\frac{6}{\sqrt{3}}\) (from the first statement) and \(AD=6*\sqrt{3}\) (from the second statement).
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 59623

If AD is 6 and ADC is a right angle, what is the area of triangular re
[#permalink]
Show Tags
27 Oct 2013, 07:03
AccipiterQ wrote: Given: \(AD=6\). Question: \(area_{ABC}=\frac{1}{2}*AD*BC=\frac{1}{2}*6*(BD+DC)=3(BD+DC)=?\) (1) Angle ABD = 60 > triangle ABD is 306090 triangle, so the sides are in ratio \(1:\sqrt{3}:2\) > as AD=6 (larger leg opposite 60 degrees angle) then \(BD=\frac{6}{\sqrt{3}}\) (smallest leg opposite 30 degrees angle). But we still don't know DC. Not sufficient. (2) AC=12, we can find DC. But we still don't know BD. Not sufficient. (1)+(2) We know both BD and DC, hence we can find area. Sufficient. Answer: C. I thought if you dropped something that was perpindicular to the base of a triangle then it was automatically a bisector; so if you found BD using (1) BD MUST equal dc, no?[/quote] Of course not. Are you saying that the height and the median in any triangle coincide? That's not true.
_________________



Director
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 563
Location: India

If AD is 6 and ADC is a right angle, what is the area of triangular re
[#permalink]
Show Tags
15 Dec 2013, 23:50
amitjash wrote: If AD is 6 and ADC is a right angle, what is the area of triangular region ABC? (1) Angle ABD = 60° (2) AC = 12 Statement I is insufficient The left triangle becomes a 90 30 60 triangle however we don't know anything about the right triangle Statement II is insufficient The right triangle becomes a 90 30 60 triangle however we don't know anything about the left triangle Combining is sufficient We know both the triangles are 90 30 60 with same sides. Hence Answer is C Pushpinder Gill
_________________
 CrackVerbal Prep Team For more info on GMAT and MBA, follow us on @AskCrackVerbal Register for the Free GMAT Kickstarter Course : http://bit.ly/2DDHKHqRegister for our Personal Tutoring Course : https://www.crackverbal.com/gmat/personaltutoring/ Join the free 4 part GMAT video training series : http://bit.ly/2DGm8tR



Intern
Joined: 30 Jan 2014
Posts: 1

If AD is 6 and ADC is a right angle, what is the area of triangular re
[#permalink]
Show Tags
06 Feb 2014, 11:28
I think answer is E, since it is not given that BDC points are collinear.



Senior Manager
Joined: 06 Aug 2011
Posts: 317

Re: If AD is 6 and ADC is a right angle, what is the area of triangular re
[#permalink]
Show Tags
18 Mar 2014, 01:11
what if question wud have been like this.. If AD is 6, and ADC is a right angle, what is the area of equilateral triangle ABC?
_________________
Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9859
Location: Pune, India

Re: If AD is 6 and ADC is a right angle, what is the area of triangular re
[#permalink]
Show Tags
18 Mar 2014, 08:51
sanjoo wrote: what if question wud have been like this..
If AD is 6, and ADC is a right angle, what is the area of equilateral triangle ABC? Then statement 1 would have been irrelevant and statement 2 would have been incorrect. If side of an equilateral triangle is 12, the altitude would be \((\sqrt{3}/2)*12 = 6*\sqrt{3}\) But AD is given to be 6.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Senior Manager
Joined: 21 Jan 2015
Posts: 453
Location: India
Concentration: Strategy, Marketing
GMAT 1: 620 Q48 V28 GMAT 2: 690 Q49 V35
WE: Sales (Consumer Products)

Re: If AD is 6 and ADC is a right angle, what is the area of triangular re
[#permalink]
Show Tags
12 Apr 2015, 17:23
Main take away from this question is: Figures are not drawn to scale.rest explanations are already given.
_________________
 The Mind is Everything, What we Think we Become.



Board of Directors
Joined: 17 Jul 2014
Posts: 2491
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

If AD is 6 and ADC is a right angle, what is the area of triangular re
[#permalink]
Show Tags
25 Oct 2016, 06:46
amitjash wrote: If AD is 6 and ADC is a right angle, what is the area of triangular region ABC? (1) Angle ABD = 60° (2) AC = 12 I tried not to solve everything as it is a DS question... Area is equal to base x height / 2 AD is height, BC is the base. We need to find the value of BC. 1. since B is 60 degree, A in ABD is 30. we have 1 leg, and we know the property of 306090 right triangle we can find BD. but since we don't know whether AD divides BC in two equal parts, then we can't tell exactly whether we can find BC. 2. AC = 12. We can find DC. we are faced with the same problem  can't find BD. 1+2 we have BD and we have DC. we can find the answer. C




If AD is 6 and ADC is a right angle, what is the area of triangular re
[#permalink]
25 Oct 2016, 06:46



Go to page
1 2
Next
[ 30 posts ]



