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

 It is currently 13 Nov 2018, 08:54

### 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

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

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### Essential GMAT Time-Management Hacks

November 14, 2018

November 14, 2018

07:00 PM PST

08:00 PM PST

Join the webinar and learn time-management tactics that will guarantee you answer all questions, in all sections, on time. Save your spot today! Nov. 14th at 7 PM PST

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

Author Message
TAGS:

### Hide Tags

Senior DS Moderator
Joined: 27 Oct 2017
Posts: 1067
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Please refer to the figure above, triangle ABC is an isosceles triang  [#permalink]

### Show Tags

03 Nov 2018, 09:05
1
4
00:00

Difficulty:

45% (medium)

Question Stats:

35% (02:10) correct 65% (02:14) wrong based on 18 sessions

### HideShow timer Statistics

Attachment:

5.jpg [ 9.71 KiB | Viewed 342 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

_________________
Manager
Joined: 16 Sep 2011
Posts: 92
Re: Please refer to the figure above, triangle ABC is an isosceles triang  [#permalink]

### Show Tags

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

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
Joined: 04 Jun 2018
Posts: 57
Re: Please refer to the figure above, triangle ABC is an isosceles triang  [#permalink]

### Show Tags

03 Nov 2018, 10:00
It cannot be calculated ans E.
Intern
Joined: 09 Apr 2018
Posts: 12
Re: Please refer to the figure above, triangle ABC is an isosceles triang  [#permalink]

### Show Tags

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
Joined: 14 Jun 2018
Posts: 180
Re: Please refer to the figure above, triangle ABC is an isosceles triang  [#permalink]

### Show Tags

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 [ 50.05 KiB | Viewed 197 times ]

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