[phpBB Debug] PHP Notice: in file /includes/check_new_recommended_questions.php on line 37: Undefined array key "last_recommended_questions_epoch"
[phpBB Debug] PHP Notice: in file /includes/check_new_recommended_questions.php on line 41: Undefined array key "last_recommended_questions_epoch"
If ABD is a triangle, is triangle ABC a right triangle : Data Sufficiency (DS)
Last visit was: 20 Jul 2024, 02:58 It is currently 20 Jul 2024, 02:58
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
SORT BY:
Date
Tags:
Show Tags
Hide Tags
avatar
Intern
Intern
Joined: 18 Apr 2011
Posts: 36
Own Kudos [?]: 241 [47]
Given Kudos: 51
Location: United States
WE:Information Technology (Computer Software)
Send PM
Most Helpful Reply
Director
Director
Joined: 03 Feb 2011
Status:Retaking after 7 years
Posts: 860
Own Kudos [?]: 4529 [12]
Given Kudos: 221
Location: United States (NY)
Concentration: Finance, Economics
GMAT 1: 720 Q49 V39
GPA: 3.75
Send PM
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30839 [10]
Given Kudos: 799
Location: Canada
Send PM
General Discussion
Intern
Intern
Joined: 04 Aug 2012
Posts: 3
Own Kudos [?]: 7 [0]
Given Kudos: 65
Location: India
Concentration: General Management, Operations
GMAT 1: 710 Q50 V35
GPA: 3.8
Send PM
Re: If ABD is a triangle, is triangle ABC a right triangle [#permalink]
joylive wrote:
If ABD is a triangle, is triangle ABC a right triangle?


(1) ACD is a right triangle.
(2) AC is the greatest side of triangle ACD.


OA not given.


The answer would be A.

Statement 1 is sufficient because:

Case 1: Angle ACD is a right angle then angle ACB has to be 180 - 90 = 90 degrees => ABC a right triangle
Case 2: Angle CAD is a right angle then both angle ADC and ACD are less than 90 degrees. Hence Angle ACB is greater than 90 degrees hence ABC is not a right triangle
Case 3: Angle ADC is a right angle then by similar logic ABC can not be a right triangle


Statement 2 is insufficient because:

if AC is the greatest side of triangle ACD then this only tells us that the angle ADC is the largest angle in the said triangle. Note that this angle CAN be 90 degree or less than or greater than 90 degree. Barring the first case we cannot conclusive say about the triangle ABC.
avatar
Intern
Intern
Joined: 18 Apr 2011
Posts: 36
Own Kudos [?]: 241 [0]
Given Kudos: 51
Location: United States
WE:Information Technology (Computer Software)
Send PM
Re: If ABD is a triangle, is triangle ABC a right triangle [#permalink]
Deepro wrote:
joylive wrote:
If ABD is a triangle, is triangle ABC a right triangle?


(1) ACD is a right triangle.
(2) AC is the greatest side of triangle ACD.


OA not given.


The answer would be A.

Statement 1 is sufficient because:

Case 1: Angle ACD is a right angle then angle ACB has to be 180 - 90 = 90 degrees => ABC a right triangle
Case 2: Angle CAD is a right angle then both angle ADC and ACD are less than 90 degrees. Hence Angle ACB is greater than 90 degrees hence ABC is not a right triangle
Case 3: Angle ADC is a right angle then by similar logic ABC can not be a right triangle


Statement 2 is insufficient because:

if AC is the greatest side of triangle ACD then this only tells us that the angle ADC is the largest angle in the said triangle. Note that this angle CAN be 90 degree or less than or greater than 90 degree. Barring the first case we cannot conclusive say about the triangle ABC.


I can see that you got 2 different answers for Statement I, so is this sufficient?
User avatar
Intern
Intern
Joined: 29 Oct 2012
Posts: 10
Own Kudos [?]: 15 [0]
Given Kudos: 5
Send PM
Re: If ABD is a triangle, is triangle ABC a right triangle [#permalink]
Deepro wrote:
joylive wrote:
If ABD is a triangle, is triangle ABC a right triangle?


(1) ACD is a right triangle.
(2) AC is the greatest side of triangle ACD.


OA not given.


The answer would be A.

Statement 1 is sufficient because:

Case 1: Angle ACD is a right angle then angle ACB has to be 180 - 90 = 90 degrees => ABC a right triangle
Case 2: Angle CAD is a right angle then both angle ADC and ACD are less than 90 degrees. Hence Angle ACB is greater than 90 degrees hence ABC is not a right triangle
Case 3: Angle ADC is a right angle then by similar logic ABC can not be a right triangle


Statement 2 is insufficient because:

if AC is the greatest side of triangle ACD then this only tells us that the angle ADC is the largest angle in the said triangle. Note that this angle CAN be 90 degree or less than or greater than 90 degree. Barring the first case we cannot conclusive say about the triangle ABC.



Hi,

Correct me if I'm wrong.

1. One of the unspoken rules in DS Questions is " The two options in the questions cannot contradict each other"
2. In your explanation for option 2, you have interpreted greatest SIDE for greatest ANGLE which are not the same.

I doubt the diagram given in the Q is imagined by the person who posted the Q initially, because clearly, in the given picture AC is not the greatest side of the triangle ACD.

In my opinion, the solution would be,

Q statement gives us the detail, that ABD and ABC are triangles.

option 1 states :

ACD is a right triangle, which means one of the three angles is 90'.INSUFFICIENT.

option 2 states:

AC is the greatest side of triangle ACD. with this we can draw a triangle ACD with AC as the hypotenuse and angle ADC = 90' ( refer diagram 1). INSUFFICIENT.

Now,
with the given data together in both the options ABC may or may not be a right triangle.( refer diagram 2 and 3). In case of 2 - yes and in case of 3 - No.
So, the answer is E. insufficient data.

plz share your inputs.

thank you.
Attachments

DS question on traingles.png
DS question on traingles.png [ 14.8 KiB | Viewed 16671 times ]


Originally posted by imk on 08 Dec 2012, 02:01.
Last edited by imk on 08 Dec 2012, 02:33, edited 1 time in total.
User avatar
Manager
Manager
Joined: 22 Dec 2011
Posts: 174
Own Kudos [?]: 1060 [0]
Given Kudos: 32
Send PM
Re: If ABD is a triangle, is triangle ABC a right triangle [#permalink]
joylive wrote:
If ABD is a triangle, is triangle ABC a right triangle?


(1) ACD is a right triangle.
(2) AC is the greatest side of triangle ACD.


OA not given.


I guess the answer has to be B

Statement 1/
Sum of the angles in a triangle = 180* & sum of ACD and ACB should equal 180*
If ACD is 90* then ACB should also be 90* - ABC a right triangle
but if DAC = 90* then other 2 angles of ACD must be less than 90* say ADC = 60 and ACD = 30 then ACB =150 and other 2 angles can be 10 and 20* - ABC is NOT a right angled triangle.

Statement 2/
IF AC is greatest side the angle at D must be greatest among the 3 angles of the triangle.
then the other 2 angles cannot be 90* or more if that's the case then ABC CANNOT BE right angled triangle. B is sufficient.

Cheers
avatar
Intern
Intern
Joined: 18 Apr 2011
Posts: 36
Own Kudos [?]: 241 [0]
Given Kudos: 51
Location: United States
WE:Information Technology (Computer Software)
Send PM
Re: If ABD is a triangle, is triangle ABC a right triangle [#permalink]
Marcab wrote:
Then why are you not posting the OA. Please do post it.



Coz I don't have the OA, if I had it, I would have already have posted it.Got these Q's somewhere and trying to get the answer myself.
User avatar
Senior Manager
Senior Manager
Joined: 06 Aug 2011
Posts: 269
Own Kudos [?]: 608 [0]
Given Kudos: 82
Send PM
Re: If ABD is a triangle, is triangle ABC a right triangle [#permalink]
joylive wrote:
Marcab wrote:
Then why are you not posting the OA. Please do post it.



Coz I don't have the OA, if I had it, I would have already have posted it.Got these Q's somewhere and trying to get the answer myself.



U shud have mentioned earlier :D
User avatar
Manager
Manager
Joined: 22 Dec 2011
Posts: 174
Own Kudos [?]: 1060 [0]
Given Kudos: 32
Send PM
Re: If ABD is a triangle, is triangle ABC a right triangle [#permalink]
sanjoo wrote:
joylive wrote:
Marcab wrote:
Then why are you not posting the OA. Please do post it.



Coz I don't have the OA, if I had it, I would have already have posted it.Got these Q's somewhere and trying to get the answer myself.



U shud have mentioned earlier :D


in fact joylive has done so. :D

Cheers
avatar
Manager
Manager
Joined: 17 Mar 2014
Posts: 61
Own Kudos [?]: 230 [0]
Given Kudos: 38
Send PM
Re: If ABD is a triangle, is triangle ABC a right triangle [#permalink]
joylive wrote:
If ABD is a triangle, is triangle ABC a right triangle?


(1) ACD is a right triangle.
(2) AC is the greatest side of triangle ACD.


OA not given.


Hi
can anybody help with this? I also think answer should be E based on imk's solution.
Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 94426
Own Kudos [?]: 642450 [0]
Given Kudos: 86335
Send PM
Re: If ABD is a triangle, is triangle ABC a right triangle [#permalink]
Expert Reply
qlx wrote:
joylive wrote:
If ABD is a triangle, is triangle ABC a right triangle?


(1) ACD is a right triangle.
(2) AC is the greatest side of triangle ACD.


OA not given.


Hi
can anybody help with this? I also think answer should be E based on imk's solution.
Thanks


The second diagram in that post is not valid. The figure in the question says that point C is on side DB, which is violated there.
avatar
Manager
Manager
Joined: 17 Mar 2014
Posts: 61
Own Kudos [?]: 230 [0]
Given Kudos: 38
Send PM
Re: If ABD is a triangle, is triangle ABC a right triangle [#permalink]
Bunuel wrote:
qlx wrote:
joylive wrote:
If ABD is a triangle, is triangle ABC a right triangle?


(1) ACD is a right triangle.
(2) AC is the greatest side of triangle ACD.


OA not given.


Hi
can anybody help with this? I also think answer should be E based on imk's solution.
Thanks


The second diagram in that post is not valid. The figure in the question says that point C is on side DB, which is violated there.


Hi thanks,
So B is the answer , I guess , can you provide the explanation if possible , or point to the best solution.
Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 94426
Own Kudos [?]: 642450 [1]
Given Kudos: 86335
Send PM
Re: If ABD is a triangle, is triangle ABC a right triangle [#permalink]
1
Kudos
Expert Reply
qlx wrote:
Bunuel wrote:
qlx wrote:
Hi
can anybody help with this? I also think answer should be E based on imk's solution.
Thanks


The second diagram in that post is not valid. The figure in the question says that point C is on side DB, which is violated there.


Hi thanks,
So B is the answer , I guess , can you provide the explanation if possible , or point to the best solution.
Thanks


Check here: if-abd-is-a-triangle-is-triangle-abc-a-right-triangle-143775.html#p1152300 or here: if-abd-is-a-triangle-is-triangle-abc-a-right-triangle-143775.html#p1152309 Please ask if anything is unclear there.
avatar
Intern
Intern
Joined: 29 Apr 2014
Posts: 2
Own Kudos [?]: [0]
Given Kudos: 2
Send PM
Re: If ABD is a triangle, is triangle ABC a right triangle [#permalink]
The answer to the question is "C". OP must have been using a study guide that ripped it from the original source and messed up the answer key.

The gist of the answer is that we are making the assumption that Angle ACD is the right angle and that line AC runs perpendicular to BD. However, taking into account both statements, we know that ABC is a right angle and AC is the hypotenuse.

Another thing, the book the question was taken from says, "The dimensions in the figure may be different from what they appear to be" underlined directly under the figure.
Math Expert
Joined: 02 Sep 2009
Posts: 94426
Own Kudos [?]: 642450 [0]
Given Kudos: 86335
Send PM
Re: If ABD is a triangle, is triangle ABC a right triangle [#permalink]
Expert Reply
HawkEye7 wrote:
The answer to the question is "C". OP must have been using a study guide that ripped it from the original source and messed up the answer key.

The gist of the answer is that we are making the assumption that Angle ACD is the right angle and that line AC runs perpendicular to BD. However, taking into account both statements, we know that ABC is a right angle and AC is the hypotenuse.

Another thing, the book the question was taken from says, "The dimensions in the figure may be different from what they appear to be" underlined directly under the figure.


I've read Nova's solution and it does not make sense. If AC is the greatest side of triangle ACD, then none of the angles of triangle AVC can be right.
avatar
Intern
Intern
Joined: 29 Apr 2014
Posts: 2
Own Kudos [?]: [0]
Given Kudos: 2
Send PM
Re: If ABD is a triangle, is triangle ABC a right triangle [#permalink]
Bunuel wrote:
I've read Nova's solution and it does not make sense. If AC is the greatest side of triangle ACD, then none of the angles of triangle AVC can be right.



I'll be honest, I half-ass read the solution and think that I got where they're coming from. It's the way I understand it that makes Choice C the best answer.

Angle D is the right-angle since AC is the longest segment of ADC. Consequently, if Angle D is the right, AC is the hypotenuse, it would make Angle C an obtuse angle greater than 90 and subsequently make angle A and B less than 90. Hence... ABC is not a right triangle.

I've probably done 300+ nova problems and one them is that you cannot take their drawings for granted.... at all. They push the "drawing may not be to scale" to the limit.
Math Expert
Joined: 02 Sep 2009
Posts: 94426
Own Kudos [?]: 642450 [0]
Given Kudos: 86335
Send PM
Re: If ABD is a triangle, is triangle ABC a right triangle [#permalink]
Expert Reply
HawkEye7 wrote:
Bunuel wrote:
I've read Nova's solution and it does not make sense. If AC is the greatest side of triangle ACD, then none of the angles of triangle AVC can be right.



I'll be honest, I half-ass read the solution and think that I got where they're coming from. It's the way I understand it that makes Choice C the best answer.

Angle D is the right-angle since AC is the longest segment of ADC. Consequently, if Angle D is the right, AC is the hypotenuse, it would make Angle C an obtuse angle greater than 90 and subsequently make angle A and B less than 90. Hence... ABC is not a right triangle.

I've probably done 300+ nova problems and one them is that you cannot take their drawings for granted.... at all. They push the "drawing may not be to scale" to the limit.


You are talking about the case when we combine the statements. I'm talking about the second statement alone.

What I'm saying is that if AC is the greatest side of triangle ACD, then none of the angles of triangle ABC can be right.

I'm not a big fan of Nova's question... Not a good source from my opinion.
avatar
Intern
Intern
Joined: 06 Jun 2014
Posts: 1
Own Kudos [?]: [0]
Given Kudos: 1
Send PM
Re: If ABD is a triangle, is triangle ABC a right triangle [#permalink]
pls can someone further explain the answer B? just dont get it! Think it should be A
avatar
Manager
Manager
Joined: 28 Apr 2014
Posts: 140
Own Kudos [?]: 74 [0]
Given Kudos: 46
Send PM
Re: If ABD is a triangle, is triangle ABC a right triangle [#permalink]
The diagram is way too misleading . I agree that in GMAT one can not assume anything in a figure but this is taking it to another level
GMAT Club Bot
Re: If ABD is a triangle, is triangle ABC a right triangle [#permalink]
 1   2   
Moderator:
Math Expert
94421 posts