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

 It is currently 17 Oct 2019, 18:38 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the

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

Hide Tags

Magoosh GMAT Instructor G
Joined: 28 Dec 2011
Posts: 4472
In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the  [#permalink]

Show Tags

1
5 00:00

Difficulty:   55% (hard)

Question Stats: 65% (02:27) correct 35% (03:03) wrong based on 92 sessions

HideShow timer Statistics

Attachment: similar triangle diagram.JPG [ 15.8 KiB | Viewed 2016 times ]

In the diagram above, BD = 5, CD = 10, and AE = 40. What is the area of the shaded region?
(A) 175
(B) 350
(C) 775
(D) 1150
(E) 1575

For a set of practice problems on Similar Geometric Figures, as well as the OE for this particular problem, see:
http://magoosh.com/gmat/2014/gmat-pract ... c-figures/

Mike _________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Intern  Joined: 30 Sep 2013
Posts: 23
Concentration: Healthcare, Technology
Re: In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the  [#permalink]

Show Tags

These are similar triangles, but small one is reversed. After noticing that, question is easily solved by proportion:
AE/BD=AC/CD=8/1

40*10*8/2 (area of big triangle) - 5*10/2 = 1575

Manager  B
Joined: 20 Feb 2013
Posts: 73
Location: India
GMAT 1: 690 Q49 V34 WE: Information Technology (Computer Software)
In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the  [#permalink]

Show Tags

1
Triangle BCD is similar to Triangle ACE having one right angle and one common angle.
Ratio of sides is 1:8, thus ratio of Area will be 1:64.

Area of BCD = (5*10)/2= 25
Area of ACE = 64*(Area of BCD) = 64*25 = 1600

Area of shaded region = Area of ACE - Area of BCD = 1600 - 25 = 1575

_________________
If my post is helpful/correct, consider giving Kudos..
Intern  B
Joined: 27 Apr 2016
Posts: 14
Location: Japan
Schools: Darden '21
Re: In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the  [#permalink]

Show Tags

How do you know that Two triangles are in ratio 1 to 8? If you take CD to be as like side with AE, the two triangles will be in ratio 1 to 4.
Senior Manager  G
Joined: 25 Feb 2019
Posts: 336
Re: In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the  [#permalink]

Show Tags

2
IMO E

As the two trinagles are similar

(area of big triangle x )/(area of small triangle y) = (ratio of corresponding sides)^2

x/25 = (8/1)^2

x = 64*25 = 1600

so area of shaded region = 1600-25 = 1575

Award kudos if helpful

Posted from my mobile device
Intern  B
Joined: 19 Feb 2019
Posts: 4
Re: In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the  [#permalink]

Show Tags

how do you conclude that they are similar triangles ? because either its SAS, AAA or SSS but here from the given question we know only one angle is equal? kindly help.
Director  D
Joined: 19 Oct 2018
Posts: 975
Location: India
Re: In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the  [#permalink]

Show Tags

1
BDC=CAE ( both are 90*), BCD=ACE (common angle in 2 triangles)
Obviously remaining angles gonna be equal.

TannyaChabbra wrote:
how do you conclude that they are similar triangles ? because either its SAS, AAA or SSS but here from the given question we know only one angle is equal? kindly help. Re: In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the   [#permalink] 30 Apr 2019, 13:36
Display posts from previous: Sort by

In the diagram, BD = 5, CD = 10, and AE = 40. What is the area of the

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

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