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

It is currently 21 Jan 2019, 15:04

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
  • GMAT Club Tests are Free & Open for Martin Luther King Jr.'s Birthday!

     January 21, 2019

     January 21, 2019

     10:00 PM PST

     11:00 PM PST

    Mark your calendars - All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday.
  • The winners of the GMAT game show

     January 22, 2019

     January 22, 2019

     10:00 PM PST

     11:00 PM PST

    In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one.

Please refer to the figure above, triangle ABC is an isosceles triang

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

Hide Tags

 
Senior DS Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1199
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Please refer to the figure above, triangle ABC is an isosceles triang  [#permalink]

Show Tags

New post 03 Nov 2018, 09:05
1
4
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

36% (02:48) correct 64% (02:32) wrong based on 23 sessions

HideShow timer Statistics

Attachment:
5.jpg
5.jpg [ 9.71 KiB | Viewed 489 times ]

Please refer to the figure above, triangle ABC is an isosceles triangle with AB = BC and BD is the perpendicular dropped from vertex B to the side AC where D is mid point of AB. Point E is marked on BD such that \(\angle\)DAE = 45 degree and \(\angle\)ECB =15 degree. What is the ratio of the area of triangle BEC to the area of the triangle ABC?


A) \(\frac{(3-√3)}{6}\)
B) \(\frac{(3+√3)}{4}\)
C) \(\frac{(5-√3)}{6}\)
D) \(\frac{(5+√3)}{3√3}\)
E) Cannot be determined

Weekly Quant Quiz #7 Question No 3


_________________

Win GMAT CLUB Test- Weekly Quant Quiz Contest
Weekly Quant Quiz Questions- Direct Download
SC: Confusable words

All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

Manager
Manager
avatar
B
Joined: 16 Sep 2011
Posts: 93
GMAT ToolKit User Reviews Badge CAT Tests
Re: Please refer to the figure above, triangle ABC is an isosceles triang  [#permalink]

Show Tags

New post 03 Nov 2018, 09:21
BD is the perpendicular bisector, hence AD= CD
moreover angle BAE = angle BCD

triangle AED and triangle EDC are similar and congruent hence angle EAD = 45= angle ECD= 60


hence ABC is a equilateral triangle , hence AB= BC= AC, lets say it is a
AD = sqrt AB*AB - AD/2*AD/2 = sqrt 3/2a

in triangle ADE,
DE =AD = a/2
hence BE = BD-DE= sqrt3 /2 a - a/2

area(triangle BEC)/ area (triangle ABC) = (1/2*CD *BE) /(sqrt 3/4 a^2) = (1/2* a/2*(sqrt3 /2- 1/2) / (sqrt3/4 a^2)= sqrt 3 - 1/sqrt 3/ 2, multiplying sqrt 3 on Numerator and Denominator
gives option A
Manager
Manager
avatar
B
Joined: 04 Jun 2018
Posts: 127
CAT Tests
Re: Please refer to the figure above, triangle ABC is an isosceles triang  [#permalink]

Show Tags

New post 03 Nov 2018, 10:00
It cannot be calculated ans E.
Intern
Intern
avatar
B
Joined: 09 Apr 2018
Posts: 17
Location: India
Schools: IIMA PGPX"20
GPA: 3.5
Re: Please refer to the figure above, triangle ABC is an isosceles triang  [#permalink]

Show Tags

New post 03 Nov 2018, 10:00
Ans is a) its a little complicated but for area of triangle bec we subtract the area of BDC-DEC
so it is (1/2 * AB/2*ABroot3/2 )-1/2*AB/2*AB/2root2
--------------------------------------------------------
root3/2 * ABsquare
Manager
Manager
avatar
G
Joined: 14 Jun 2018
Posts: 223
Re: Please refer to the figure above, triangle ABC is an isosceles triang  [#permalink]

Show Tags

New post 04 Nov 2018, 01:05
ABC is an equilateral triangle.
Assume side = 10
Area of ABC = 25√3

BD = 10√3 / 2 = 5√3
BD = BE + ED
BE = 5√3 - 5 = 5(√3 - 1)

Area of BEA = 1/2 * BE * DC = 25(√3 - 1) / 2

BEA / ABC = 25(√3 - 1) / 2* 25√3

= (√3 - 1)/ 2√3
Multiply num and deno with √3
3-√3 / 6

A
Attachments

q3.PNG
q3.PNG [ 50.05 KiB | Viewed 340 times ]

GMAT Club Bot
Re: Please refer to the figure above, triangle ABC is an isosceles triang &nbs [#permalink] 04 Nov 2018, 01:05
Display posts from previous: Sort by

Please refer to the figure above, triangle ABC is an isosceles triang

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


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®.