GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 18 Jan 2019, 14:16

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
Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • Free GMAT Strategy Webinar

     January 19, 2019

     January 19, 2019

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
  • FREE Quant Workshop by e-GMAT!

     January 20, 2019

     January 20, 2019

     07:00 AM PST

     07:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

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

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52285
In the figure above, D is a point on side AC of ΔABC. Is ΔABC is isosc  [#permalink]

Show Tags

New post 09 Dec 2014, 14:39
1
8
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

61% (01:11) correct 39% (01:01) wrong based on 197 sessions

HideShow 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


Kudos for a correct solution.

Attachment:
triang ABCD.JPG
triang ABCD.JPG [ 3.38 KiB | Viewed 4378 times ]

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Most Helpful Community Reply
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2638
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Re: In the figure above, D is a point on side AC of ΔABC. Is ΔABC is isosc  [#permalink]

Show Tags

New post 25 Jul 2015, 04:00
5
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.

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 3291 times ]

General Discussion
Manager
Manager
avatar
Joined: 22 Sep 2012
Posts: 129
Concentration: Strategy, Technology
WE: Information Technology (Computer Software)
Re: In the figure above, D is a point on side AC of ΔABC. Is ΔABC is isosc  [#permalink]

Show Tags

New post 09 Dec 2014, 19:53
2
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
Intern
Intern
User avatar
Joined: 08 Jul 2012
Posts: 47
Re: In the figure above, D is a point on side AC of ΔABC. Is ΔABC is isosc  [#permalink]

Show Tags

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 3694 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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52285
Re: In the figure above, D is a point on side AC of ΔABC. Is ΔABC is isosc  [#permalink]

Show Tags

New post 26 Dec 2014, 10:01
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.

Attachment:
triang ABCD.JPG


The correct answer is B.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 07 Apr 2015
Posts: 164
Re: In the figure above, D is a point on side AC of ΔABC. Is ΔABC is isosc  [#permalink]

Show Tags

New post 25 Jul 2015, 01:43
What exactly does this "BD┴AC" say?

I don't know what the symbol means.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52285
Re: In the figure above, D is a point on side AC of ΔABC. Is ΔABC is isosc  [#permalink]

Show Tags

New post 25 Jul 2015, 01:44
Retired Moderator
User avatar
S
Joined: 18 Sep 2014
Posts: 1114
Location: India
GMAT ToolKit User Premium Member Reviews Badge
In the figure above, D is a point on the side AC of ΔABC.Is ΔABC isos?  [#permalink]

Show Tags

New post 20 Feb 2016, 08:42
Attachment:
1.png
1.png [ 16.33 KiB | Viewed 2889 times ]


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.
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2638
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
In the figure above, D is a point on the side AC of ΔABC.Is ΔABC isos?  [#permalink]

Show Tags

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.
Intern
Intern
User avatar
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]

Show Tags

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/)

Senior DS Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1195
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: In the figure above, D is a point on the side AC of ΔABC.Is ΔABC isos?  [#permalink]

Show Tags

New post 26 Dec 2018, 07:54
Intern
Intern
avatar
B
Joined: 30 May 2018
Posts: 7
Re: In the figure above, D is a point on the side AC of ΔABC.Is ΔABC isos?  [#permalink]

Show Tags

New post 12 Jan 2019, 09:10
Bunuel VeritasKarishma chetan2u Cant option B result in equilateral triangle?
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7201
Re: In the figure above, D is a point on the side AC of ΔABC.Is ΔABC isos?  [#permalink]

Show Tags

New post 12 Jan 2019, 09:33
1
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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

GMAT Club Bot
Re: In the figure above, D is a point on the side AC of ΔABC.Is ΔABC isos? &nbs [#permalink] 12 Jan 2019, 09:33
Display posts from previous: Sort by

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

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


cron
Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.