Find all School-related info fast with the new School-Specific MBA Forum

It is currently 01 Sep 2014, 05:48

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

DS Geometry (m08q22)

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
1 KUDOS received
Intern
Intern
avatar
Joined: 12 Feb 2006
Posts: 29
Followers: 0

Kudos [?]: 3 [1] , given: 0

GMAT Tests User
DS Geometry (m08q22) [#permalink] New post 23 Apr 2006, 08:25
1
This post received
KUDOS
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

46% (01:36) correct 54% (00:56) wrong based on 413 sessions
If M , N , and O are midpoints of sides AB , BC , and AC of triangle ABC . What is the area of triangle MON ?

1. The area of ABC is \frac{\sqrt{3}}{4}
2. ABC is an equilateral triangle with height \frac{sqrt3}{2}

[Reveal] Spoiler: OA
D

Source: GMAT Club Tests - hardest GMAT questions

Please explain your answer. Thank You.
[Reveal] Spoiler: OA
Kaplan GMAT Prep Discount CodesKnewton GMAT Discount CodesGMAT Pill GMAT Discount Codes
1 KUDOS received
Intern
Intern
avatar
Joined: 19 Feb 2006
Posts: 46
Followers: 1

Kudos [?]: 1 [1] , given: 0

 [#permalink] New post 23 Apr 2006, 09:17
1
This post received
KUDOS
Since M, N, and O are midpoints of sides AB, BC, and AC of triangle ABC,

Area of AMO = Area of BMN = Area of CNO = Area of MNO = Area of ABC/4

Area of MNO = sqrt(3)/16

(1) is sufficient

Again (2) also sufficient as we know area of an equilateral triangle = sqrt(3)*a^2/4 where a is the side and height is sqrt(3)*a/2

hence a = 1 and Area of ABC = sqrt(3)/4

The answer is D
Director
Director
User avatar
Joined: 04 Jan 2006
Posts: 928
Followers: 1

Kudos [?]: 12 [0], given: 0

GMAT Tests User
 [#permalink] New post 23 Apr 2006, 10:25
1 is sufficiient only if ABC is equilateral triangle.. and thats not said..
was wondering if the area says that is equilateral..
Director
Director
User avatar
Joined: 04 Jan 2006
Posts: 928
Followers: 1

Kudos [?]: 12 [0], given: 0

GMAT Tests User
 [#permalink] New post 23 Apr 2006, 10:27
I would go with B..

if ABC is equilateral, then area of mno is 1/4th of abc..

1) says area is sqrt3/4... which is base *height = sqrt3/2.. which gives many possibilites for base.
VP
VP
User avatar
Joined: 29 Apr 2003
Posts: 1408
Followers: 2

Kudos [?]: 15 [0], given: 0

GMAT Tests User
 [#permalink] New post 23 Apr 2006, 13:40
Answer is D. The midpoints essentially divide the triangle into 4 equal aread triangles.
Director
Director
User avatar
Joined: 08 Jun 2004
Posts: 502
Location: Europe
Followers: 1

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

GMAT Tests User
 [#permalink] New post 24 Apr 2006, 04:08
AgreeD.

Guys would you please remaind me how to find the area of the equilateral (or any triangle) triangle knowing only the height? Thank you.
Director
Director
User avatar
Joined: 04 Jan 2006
Posts: 928
Followers: 1

Kudos [?]: 12 [0], given: 0

GMAT Tests User
 [#permalink] New post 24 Apr 2006, 16:44
h = a*sqrt(3)/2
area of equi = sqrt(3)a*a/4
Retired Moderator
User avatar
Joined: 18 Jul 2008
Posts: 997
Followers: 8

Kudos [?]: 66 [0], given: 5

GMAT Tests User
Re: DS Geometry [#permalink] New post 28 Nov 2008, 14:52
Does anyone have a better explanation for this?

My 2 questions are:

1) how do we prove that triangle ABC is divided into equal 4 smaller triangles by knowing the midpoints.

2) How do we find the area of MON if we only know the height of ABC.
Manager
Manager
avatar
Joined: 27 May 2008
Posts: 204
Followers: 1

Kudos [?]: 14 [0], given: 0

GMAT Tests User
Re: DS Geometry [#permalink] New post 28 Nov 2008, 20:13
Hi Yach,

1 - cant be proved by just knowing midpoint. we need height and sides of the triangle. With Area we cant prove unless it is an equilateral triangle.

2) we know h = V3/2 * Side for equilateral triangle
so side = 1 in our case since h = V3/2

Area of MON = 1/4 of Area ABC. since equilateral.
Director
Director
avatar
Joined: 29 Aug 2005
Posts: 881
Followers: 7

Kudos [?]: 150 [0], given: 7

GMAT Tests User
Re: DS Geometry [#permalink] New post 15 Feb 2009, 02:52
I agree that the answer should be D.

In the link below, I found explanation showing that a triangle formed by connecting midpoints of the triangle divides the area of this bigger triangle into 4 equal areas:
http://mathworld.wolfram.com/MedialTriangle.html
Expert Post
1 KUDOS received
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3571
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 358

Kudos [?]: 1758 [1] , given: 358

GMAT ToolKit User GMAT Tests User Premium Member
Re: DS Geometry [#permalink] New post 15 Feb 2009, 03:37
1
This post received
KUDOS
Expert's post
yach wrote:
M, N, and O are midpoints of sides AB, BC, and AC of triangle ABC. What is the area of triangle MON?

The main idea here is realizing that S_{MON}=\frac14*S_{ABC}

1. Let's consider vertex A: M and O are midpoints of AB and AC. In other words, all linear sizes of MAO triangle is smaller by 2 times than all linear sizes of BAC. Therefore,S_{MAO}=\frac14*S_{ABC}

2. Applying the same reasoning for each vertex we will get:
S_{MON}=S_{ABC} - (S_{MAO}+S_{MBN}+S_{NCO}) = S_{ABC} - (\frac14*S_{ABC}+\frac14*S_{ABC}+\frac14*S_{ABC}) =\frac14*S_{ABC}
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Manager
Manager
avatar
Joined: 02 Aug 2007
Posts: 232
Schools: Life
Followers: 3

Kudos [?]: 26 [0], given: 0

GMAT Tests User
Re: DS Geometry [#permalink] New post 15 Feb 2009, 15:24
walker wrote:
yach wrote:
M, N, and O are midpoints of sides AB, BC, and AC of triangle ABC. What is the area of triangle MON?

The main idea here is realizing that S_{MON}=\frac14*S_{ABC}


But how do you arrive at this conclusion, were are not told that either ABC or MNO are equilateral.
AB, BC, and OC can each be a different length, as can MN, ON, OM.
CEO
CEO
User avatar
Joined: 29 Aug 2007
Posts: 2501
Followers: 53

Kudos [?]: 500 [0], given: 19

GMAT Tests User
Re: DS Geometry [#permalink] New post 15 Feb 2009, 21:40
xALIx wrote:
walker wrote:
yach wrote:
M, N, and O are midpoints of sides AB, BC, and AC of triangle ABC. What is the area of triangle MON?

The main idea here is realizing that S_{MON}=\frac14*S_{ABC}


But how do you arrive at this conclusion, were are not told that either ABC or MNO are equilateral.
AB, BC, and OC can each be a different length, as can MN, ON, OM.


This is good reference: http://mathworld.wolfram.com/MedialTriangle.html

Mid point therom says that a triangle made from connecting mid-points of the sides of a given triangle is 1/4 of the original triangle. In that case, it is not required to be equilateral.
_________________

Verbal: new-to-the-verbal-forum-please-read-this-first-77546.html
Math: new-to-the-math-forum-please-read-this-first-77764.html
Gmat: everything-you-need-to-prepare-for-the-gmat-revised-77983.html


GT

2 KUDOS received
Director
Director
avatar
Joined: 27 May 2008
Posts: 552
Followers: 5

Kudos [?]: 171 [2] , given: 0

GMAT Tests User
Re: DS Geometry [#permalink] New post 15 Feb 2009, 21:56
2
This post received
KUDOS
for any triangle, ABC if you join mid points and divide it into 4 parts, the area will be divided into 4 triangles with each having an area equal to 1/4 of triangle ABC.

Lets prove is with simple method, visualize the triangle ABC on co-ordinate plane

A = (0,0)
B = (x,0)
C = (a,b)

Area = xb/2 (Note that area does not depend on a)

M = (x/2, 0)
N = ((x+a)/2, b/2)
O = (a/2, b/2)

base of triangle, NO = x/2
Height = b/2
Area of MNO = xb/8

Similarly triangle AMO
base AM = x/2
height = b/2
Area = xb/8
Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3571
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 358

Kudos [?]: 1758 [0], given: 358

GMAT ToolKit User GMAT Tests User Premium Member
Re: DS Geometry [#permalink] New post 15 Feb 2009, 23:01
Expert's post
xALIx wrote:
But how do you arrive at this conclusion, were are not told that either ABC or MNO are equilateral.
AB, BC, and OC can each be a different length, as can MN, ON, OM.


This problem test similarity. ABC and MAO (as other small triangles) are similar triangles: the same angle A and the same relation between AB/AC=AM/AO.
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Intern
Intern
avatar
Joined: 22 Dec 2009
Posts: 22
Followers: 0

Kudos [?]: 7 [0], given: 1

Re: DS Geometry (m08q22) [#permalink] New post 03 Sep 2010, 09:34
Please explain how 2 is sufficient. I know how to get the area of an equilateral but a bit puzzled as we are only given the height
Director
Director
User avatar
Status: My Thread Master Bschool Threads-->Krannert(Purdue),WP Carey(Arizona),Foster(Uwashngton)
Joined: 27 Jun 2011
Posts: 894
Followers: 58

Kudos [?]: 150 [0], given: 57

GMAT ToolKit User Reviews Badge
Re: [#permalink] New post 30 Nov 2011, 08:41
willget800 wrote:
I would go with B..

if ABC is equilateral, then area of mno is 1/4th of abc..

1) says area is sqrt3/4... which is base *height = sqrt3/2.. which gives many possibilites for base.


Even i selected B....but this weblink is a good solution to this mistake

http://mathworld.wolfram.com/MedialTriangle.html
_________________

General GMAT useful links-->

Indian Bschools Accepting Gmat | My Gmat Daily Diary | All Gmat Practice CAT's | MBA Ranking 2013 | How to Convert Indian GPA/ Percentage to US 4 pt. GPA scale | GMAT MATH BOOK in downloadable PDF format| POWERSCORE CRITICAL REASONING BIBLE - FULL CHAPTER NOTES | Result correlation between GMAT and GMAT Club's Tests | Best GMAT Stories - Period!

More useful links-->

GMAT Prep Software Analysis and What If Scenarios| GMAT and MBA 101|Everything You Need to Prepare for the GMAT|New to the GMAT Club? <START HERE>|GMAT ToolKit: iPhone/iPod/iPad/Android application|

Verbal Treasure Hunt-->

"Ultimate" Study Plan for Verbal on the GMAT|Books to Read (Improve Verbal Score and Enjoy a Good Read)|Best Verbal GMAT Books 2012|Carcass Best EXTERNAL resources to tackle the GMAT Verbal Section|Ultimate GMAT Grammar Book from GC club [Free Download]|Ultimate Sentence Correction Encyclopedia|Souvik's The Most Comprehensive Collection Of Everything Official-SC|ALL SC Rules+Official Qs by Experts & Legendary Club Members|Meaning/Clarity SC Question Bank by Carcass_Souvik|Critical Reasoning Shortcuts and Tips|Critical Reasoning Megathread!|The Most Comprehensive Collection Of Everything Official- CR|GMAT Club's Reading Comprehension Strategy Guide|The Most Comprehensive Collection Of Everything Official- RC|Ultimate Reading Comprehension Encyclopedia|ALL RC Strategy+Official Q by Experts&Legendary Club Members

----
---
--
-


1 KUDOS = 1 THANK


Kick Ass Gmat

Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 25227
Followers: 3428

Kudos [?]: 25197 [2] , given: 2702

Re: DS Geometry (m08q22) [#permalink] New post 22 Apr 2012, 05:18
2
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
yach wrote:
If M , N , and O are midpoints of sides AB , BC , and AC of triangle ABC . What is the area of triangle MON ?

1. The area of ABC is \frac{\sqrt{3}}{4}
2. ABC is an equilateral triangle with height \frac{sqrt3}{2}

[Reveal] Spoiler: OA
D

Source: GMAT Club Tests - hardest GMAT questions

Please explain your answer. Thank You.


Look at the diagram below:

Image
MN, NO and OM each are midsegments of triangle ABC (midsegment is a line segment joining the midpoints of two sides of a triangle). Important property of a midsegment: the midsegment is always half the length of the third side. So, MN=\frac{AC}{2}, NO=\frac{AB}{2} and OM=\frac{BC}{2}

Next, since each side of triangle MNO is half of the side of triangle ABC then these triangles are similar (the ratio of all the sides are the same). Important property of similar triangles: if two similar triangles have sides in the ratio \frac{x}{y}, then their areas are in the ratio \frac{x^2}{y^2}.

Since the sides of two similar triangles MNO and ABC are in the ratio 1:2 then then their areas are in the ratio 1:4 --> (area of MNO)=(area of ABC)/4.

So, in order to find the area of MNO we should find the area of ABC.

(1) The area of ABC is \frac{\sqrt{3}}{4}. Sufficient.
(2) ABC is an equilateral triangle with height \frac{sqrt3}{2} --> we can find the area of equilateral triangle with given altitude. Sufficient.

Answer: D.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 07 Sep 2011
Posts: 74
GMAT 1: 660 Q41 V40
GMAT 2: 720 Q49 V39
WE: Analyst (Mutual Funds and Brokerage)
Followers: 1

Kudos [?]: 22 [0], given: 13

Re: DS Geometry (m08q22) [#permalink] New post 28 Aug 2012, 09:52
Based on the prompt, We know that the each side of triangle MON is going to be exactly HALF the length of the corresponding sides of triangle ABC. Which means that these two are SIMILAR triangles, and we will be able to figure out the area of MON if we are given the area of ABC. based on the ratio s^2:s^2 (s=side).

1) SUFFICIENT.
2) if ABC is an equilateral triangle, its height is the same from any base, and also cuts the triangle ABC in half to make it 2 right triangles with sides ratio of x:x^(1/2):2x. Knowing the side of the longest leg, we are able to calculate the rest of the sides and hence the area of ABC. SUFFICIENT.

Answer is
[Reveal] Spoiler:
D.


PS: Notice that I did not actually do any calculations in this problem. It was all conceptual.
Intern
Intern
User avatar
Status: Looking for High GMAT Score
Joined: 19 May 2012
Posts: 37
Location: India
Concentration: Strategy, Marketing
WE: Marketing (Internet and New Media)
Followers: 0

Kudos [?]: 5 [0], given: 58

Re: DS Geometry (m08q22) [#permalink] New post 28 Aug 2012, 22:09
I got answer but was able to solve,as both equations tells the same things answer D
_________________

“The best time to plant a tree was 20 years ago. The second best time is now.” – Chinese Proverb

Re: DS Geometry (m08q22)   [#permalink] 28 Aug 2012, 22:09
    Similar topics Author Replies Last post
Similar
Topics:
10 Experts publish their posts in the topic DS Geometry (m08q22) yach 20 23 Apr 2006, 08:25
DS- Geometry vikramm 2 19 Oct 2005, 19:09
DS - Geometry AJB77 5 05 Jul 2005, 08:17
DS: Geometry gayathri 4 14 Dec 2004, 07:12
DS: Geometry gayathri 8 07 Dec 2004, 15:57
Display posts from previous: Sort by

DS Geometry (m08q22)

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page    1   2    Next  [ 21 posts ] 

Moderators: WoundedTiger, Bunuel



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

Powered by phpBB © phpBB Group and phpBB SEO

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®.