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

It is currently 18 Nov 2018, 00:59

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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
  • The winning strategy for 700+ on the GMAT

     November 20, 2018

     November 20, 2018

     06:00 PM EST

     07:00 PM EST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

In the figure above, segment BD has length 6. What is the length

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

Hide Tags

Manager
Manager
avatar
P
Joined: 14 Mar 2011
Posts: 143
GMAT 1: 760 Q50 V42
Premium Member Reviews Badge
In the figure above, segment BD has length 6. What is the length  [#permalink]

Show Tags

New post 30 Mar 2017, 21:37
16
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

31% (02:12) correct 69% (02:30) wrong based on 137 sessions

HideShow timer Statistics

Attachment:
Capture.PNG
Capture.PNG [ 3.26 KiB | Viewed 1895 times ]


In the figure above, segment BD has length 6. What is the length of segment AC?
A. The area of quadrilateral ABCD is 60.
B. The length of segment AD is 10.

_________________

If you find my posts/replies helpful, please take a moment to click on the "kudos" icon.

Most Helpful Community Reply
Director
Director
User avatar
S
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 526
Location: India
GMAT 1: 780 Q51 V46
Re: In the figure above, segment BD has length 6. What is the length  [#permalink]

Show Tags

New post 30 Mar 2017, 23:34
5
Top Contributor
1
Hi Godot53,

One cardinal rule that will serve you well while solving Geometry questions on the GMAT is to 'never make assumptions'. While solving Ds questions, do not go by how the diagram looks to you, but instead look for definite pieces of information provided in the questions stem and the diagram.

The definite pieces of information provided here are
1. Angle ABD and BDC are 90 degrees

If we analyze this piece of information in depth, then we can definitely say that the lines AB and DC are parallel. When a transversal (in this case BD) cuts two lines (in this case AB and DC), the two lines are said to be parallel if ONE of the three conditions are satisfied:

1. Alternate angles are equal
2. Corresponding angles are equal
3. Sum of the interior angles is 180 degrees

Attachment:
Screenshot.png
Screenshot.png [ 38.79 KiB | Viewed 1864 times ]


So here since we have angles ABD and BDC to be 90 degrees, the sum of interior angles will be 180 degrees. This makes lines AB and DC parallel.

ABCD is therefore a trapezoid whose bases are AB and CD and whose perpendicular height is BD=6.

Area of a trapezoid = (Sum of parallel sides)/2 * h

Thus, area of trapezoid ABCD = (AB+CD)/2 * 6 = 3(AB+CD)

Attachment:
Screenshot 2.PNG
Screenshot 2.PNG [ 14.34 KiB | Viewed 1864 times ]


In the figure above, since AO is perpendicular to CO, quadrilateral ABDO is a rectangle and ∆ACO is a right triangle

In rectangle ABDO, AO = BD =6 and DO = AB.

OC = OD+CD ------> OC = AB + DC .

Since ∆ACE is a right triangle, AO^2 + OC^2 = AC^2 ------> 6^2 + OC^2 = AC^2.

So here we just need the length of OC or the length of AB + DC.

Statement 1: The area of quadrilateral ABCD is 60

3(AB+CD) = 60
AB+CD = 20. SUFFICIENT.

Statement 2: AD =10


Using this information we can find out AB, but we still do not know the length of DC. INSUFFICIENT.

Answer : A

Hope this helps!

CrackVerbal Academics Team
_________________

For more info on GMAT and MBA, follow us on @AskCrackVerbal

General Discussion
ISB, NUS, NTU Moderator
User avatar
G
Joined: 11 Aug 2016
Posts: 312
Reviews Badge CAT Tests
Re: In the figure above, segment BD has length 6. What is the length  [#permalink]

Show Tags

New post 25 Aug 2018, 21:43
Given: BD=6

Statement 1: The area of quadrilateral ABCD is 60.
Let the point where AC intersects BD be X. So, BD= BX + XD

The area of quadrilateral ABCD= Area of Triangle ABC + Area of Triangle ADC
Area of Triangle ABC= (1/2)*AC*BX
Area of Triangle ADC= (1/2)*AC*XD

On Adding, we get
Area of Triangle ABC + Area of Triangle ADC= (1/2)*AC*BX + (1/2)*AC*XD
Taking (1/2)*AC Common, we get
The area of quadrilateral ABCD= Area of Triangle ABC + Area of Triangle ADC= (1/2)*AC*[BX+DX]
60 = (1/2)*AC*BD
60= (1/2)*AC*6

We can solve for AC.
Hence, Sufficient.

Statement 1:The length of segment AD is 10.

Using AD, we can Find BC but nothing else.
hence Insufficient.

Therefore, our Answer is A.

godot53 wrote:
Attachment:
Capture.PNG


In the figure above, segment BD has length 6. What is the length of segment AC?
A. The area of quadrilateral ABCD is 60.
B. The length of segment AD is 10.

_________________

~R.
If my post was of any help to you, You can thank me in the form of Kudos!!

GMAT Club Bot
Re: In the figure above, segment BD has length 6. What is the length &nbs [#permalink] 25 Aug 2018, 21:43
Display posts from previous: Sort by

In the figure above, segment BD has length 6. What is the length

  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®.