GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
close
It is currently 13 Jun 2021, 22:01
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
New comers' posts

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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
In the figure above, D is a point on the side AC of ΔABC.Is ΔABC isos?
11 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
Tags:
Find Similar Topics 

Show Tags
Hide Tags

User avatar
V
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 76961
Premium Member CAT Tests Top Member of the Month
In the figure above, D is a point on the side AC of ΔABC.Is ΔABC isos? [#permalink] New post  09 Dec 2014, 14:39
2
Kudos
34
Bookmarks
Expert Reply
Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

65% (01:45) correct 35% (01:43) wrong based on 557 sessions

Hide Show timer Statistics

Tough and Tricky questions: Geometry.



Image
In the figure above, D is a point on side AC of ΔABC. Is ΔABC is isosceles?

(1) The area of triangular region ABD is equal to the area of triangular region DBC.
(2) BD┴AC and AD = DC




Show Spoiler
Attachment:
triang ABCD.JPG
triang ABCD.JPG [ 3.38 KiB | Viewed 10675 times ]
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.

_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
Most Helpful Community Reply
avatar
G
ENGRTOMBA2018
SVP
SVP
Joined: 20 Mar 2014
Posts: 2479
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
GMAT ToolKit User Reviews Badge
Re: In the figure above, D is a point on the side AC of ΔABC.Is ΔABC isos? [#permalink] New post  25 Jul 2015, 04:00
6
Kudos
2
Bookmarks
Bunuel wrote:

Tough and Tricky questions: Geometry.



Image
In the figure above, D is a point on side AC of ΔABC. Is ΔABC is isosceles?

(1) The area of triangular region ABD is equal to the area of triangular region DBC.
(2) BD┴AC and AD = DC


Kudos for a correct solution.

Show Spoiler
Attachment:
The attachment triang ABCD.JPG is no longer available


Per statement 1, Area Triangle (BAD} = Area Triangle {BDC}

---> 0.5*BE*AD = 0.5*BE*CD ---> AD = CD . But no information about AB and BC. Thus this triangle may or may not be isosceles. Thus this statement is not sufficient.

Per statement 2, BD┴AC and AD = DC ---> Triangles BDA and BDC are congruent. ---> AB = BC ---> Triangle ABC is isosceles. Thus this statement is sufficient.

B is the correct answer.
Attachments

2015-07-25_7-55-54.jpg
2015-07-25_7-55-54.jpg [ 20.54 KiB | Viewed 8894 times ]


_________________
My Kellogg Journey (2016-2018): https://gmatclub.com/forum/my-kellogg-journey-325661.html
Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html
Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html
Signature Read More
General Discussion
avatar
kinghyts
Manager
Manager
Joined: 22 Sep 2012
Posts: 117
Concentration: Strategy, Technology
WE:Information Technology (Computer Software)
Re: In the figure above, D is a point on the side AC of ΔABC.Is ΔABC isos? [#permalink] New post  09 Dec 2014, 19:53
1
Kudos
2
Bookmarks
Statement 1: The area of triangular region ABD is equal to the area of triangular region DBC.

This means that the point D is mid-point of AC. But, we can't still say whether the triangle ABC is isosceles or not. Insufficient.

Statement 2: BD┴AC and AD = DC. Signifies that the median drawn from the vertex B is a perpendicular bisector. This can only happen if the triangle is isosceles triangle with AB = BC. Sufficient

The answer should be B
User avatar
JJo
Intern
Intern
Joined: 08 Jul 2012
Posts: 45
Re: In the figure above, D is a point on the side AC of ΔABC.Is ΔABC isos? [#permalink] New post  10 Dec 2014, 04:24
In the figure above, D is a point on side AC of ΔABC. Is ΔABC is isosceles?

(1) The area of triangular region ABD is equal to the area of triangular region DBC --> this gives us info that D is the midpoint of AC but we don't have any info about angle ADB & BDC....insufficient
(2) BD┴AC and AD = DC --> this gives us info that D is midpoint of AC and that BD┴AC, this condition will make AB=BC.......sufficient.(refer below image, hope my understanding is correct :? )

Ans. B)
Attachments

File comment: triangle
triangle.png
triangle.png [ 7.79 KiB | Viewed 9226 times ]


_________________
Our greatest weakness lies in giving up. The most certain way to succeed is always to try just one more time. - Thomas A. Edison
Signature Read More
avatar
noTh1ng
Manager
Manager
Joined: 07 Apr 2015
Posts: 143
Re: In the figure above, D is a point on the side AC of ΔABC.Is ΔABC isos? [#permalink] New post  25 Jul 2015, 01:43
What exactly does this "BD┴AC" say?

I don't know what the symbol means.
User avatar
V
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 76961
Premium Member CAT Tests Top Member of the Month
Re: In the figure above, D is a point on the side AC of ΔABC.Is ΔABC isos? [#permalink] New post  25 Jul 2015, 01:44
1
Kudos
Expert Reply
noTh1ng wrote:
What exactly does this "BD┴AC" say?

I don't know what the symbol means.


It means that BD is perpendicular to AC.
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
avatar
G
ENGRTOMBA2018
SVP
SVP
Joined: 20 Mar 2014
Posts: 2479
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
GMAT ToolKit User Reviews Badge
Re: In the figure above, D is a point on the side AC of ΔABC.Is ΔABC isos? [#permalink] New post  20 Feb 2016, 09:03
Nevernevergiveup wrote:
Attachment:
1.png


In the figure above, D is a point on the side AC of ΔABC. Is ΔABC isosceles?

(1) The area of the triangular region ABD is equal to the area of triangular region DBC.

(2) BD is perpendicular to AC and AD = DC.


Statement 1 is straightforward to see that it is NOT sufficient. The most this statement will do is to provide a scenario when we have AD=CD. But this does not yet answer the question asked.

Statement 2, is tricky as in from the figure provided, BD can either be to the left of A or between A and C or to the right of C. But in only 1 case (of between A and C) will you get AD=CD such that BD \(\perp\) AC. With this scenario, triangle ABC is indeed isosceles (by making triangles ABD and BCD congruent to each other by the SAS property ---> AB=BC) . Hence sufficient.

B is the correct answer.

Hope this helps.
_________________
My Kellogg Journey (2016-2018): https://gmatclub.com/forum/my-kellogg-journey-325661.html
Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html
Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html
Signature Read More
User avatar
sydneygmat1
Intern
Intern
Joined: 17 Feb 2016
Posts: 7
Re: In the figure above, D is a point on the side AC of ΔABC.Is ΔABC isos? [#permalink] New post  20 Feb 2016, 17:46
Answer: B

We are after: Is ΔABC isosceles?

(1) Not sufficient. Using the formula for areas of triangle, we get


Area of ΔABD = Area of ΔABD
1/2 * AD * h = 1/2 * DC * h

h is the height for both triangles, if you drop a perpendicular from point B on AC. This will fall on the extended AC (if you can imagine it)

The above equation yields to:
AD = AC

But we want to know if ΔABC is isosceles. This information doesn't help so it is INSUFFICIENT.

(2) Sufficient

Since BD ⊥AC, and D is on AC, imagine D dividing AC into two sides i.e. AD =AC.

Now imagine two right angled Δs inside ABC being split in the middle by BD. These two right angled Δs have the same base and height so the hypotenuse will be same i.e. AB = AC
_________________
Fahd

Chief Tutor

Sydney GMAT (http://www.sydneygmat.com/)
Signature Read More
avatar
B
Bishal123456789
Intern
Intern
Joined: 30 May 2018
Posts: 31
Schools: SSE Int'l Business CEMS MiM "22 (S), ESSEC MiM "22 (S)
Re: In the figure above, D is a point on the side AC of ΔABC.Is ΔABC isos? [#permalink] New post  12 Jan 2019, 09:10
Bunuel VeritasKarishma chetan2u Cant option B result in equilateral triangle?
User avatar
V
chetan2u
Math Expert
Joined: 02 Aug 2009
Posts: 9991
Reviews Badge Top Member of the Month
Re: In the figure above, D is a point on the side AC of ΔABC.Is ΔABC isos? [#permalink] New post  12 Jan 2019, 09:33
3
Kudos
Expert Reply
Bishal123456789 wrote:
Bunuel VeritasKarishma chetan2u Cant option B result in equilateral triangle?



Hi Bishal,

Yes, it CAN be an equilateral triangle....
Of course, it is an isosceles triangle for sure.. also all equilateral triangles are Isosceles
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 19420
Re: In the figure above, D is a point on the side AC of ΔABC.Is ΔABC isos? [#permalink] New post  01 Sep 2020, 06:04
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.
_________________
GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources
Signature Read More
GMAT Club Bot
gmatclubot
Re: In the figure above, D is a point on the side AC of ΔABC.Is ΔABC isos? [#permalink]
01 Sep 2020, 06:04
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderators:
chetan2u
Math Expert
9991 posts
Bunuel
Math Expert
76961 posts
GMATBusters
Retired Moderator
2005 posts
nick1816
DS Forum Moderator
2290 posts

cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions