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

 It is currently 18 Feb 2019, 14:45

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Valentine's day SALE is on! 25% off.

February 18, 2019

February 18, 2019

10:00 PM PST

11:00 PM PST

We don’t care what your relationship status this year - we love you just the way you are. AND we want you to crush the GMAT!
• ### Get FREE Daily Quiz for 2 months

February 18, 2019

February 18, 2019

10:00 PM PST

11:00 PM PST

Buy "All-In-One Standard (\$149)", get free Daily quiz (2 mon). Coupon code : SPECIAL

# In a trapezium ABCD, AB is parallel to DC, AB = 3DC, and the diagonals

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52938
In a trapezium ABCD, AB is parallel to DC, AB = 3DC, and the diagonals  [#permalink]

### Show Tags

31 Jul 2016, 02:08
00:00

Difficulty:

65% (hard)

Question Stats:

55% (01:51) correct 45% (02:03) wrong based on 175 sessions

### HideShow timer Statistics

In a trapezium ABCD, AB is parallel to DC, AB = 3*DC, and the diagonals of the trapezium intersect at O. The ratio of the area of ∆OCD to the area of ∆OAB is:

(A) 1:9
(B) 1:3
(C) 3:1
(D) 1:10
(E) Cannot be determined

_________________
Senior Manager
Joined: 02 Mar 2012
Posts: 297
Schools: Schulich '16
Re: In a trapezium ABCD, AB is parallel to DC, AB = 3DC, and the diagonals  [#permalink]

### Show Tags

31 Jul 2016, 02:56
triangles are similar , so ratio will be 1:9

A
Intern
Joined: 28 Mar 2014
Posts: 9
Re: In a trapezium ABCD, AB is parallel to DC, AB = 3DC, and the diagonals  [#permalink]

### Show Tags

31 Jul 2016, 22:58
Can someone please explain how the diagonal properties of trapezoid. I am not sure how the two triangles would be similar in this case
Senior Manager
Joined: 11 Nov 2014
Posts: 331
Location: India
WE: Project Management (Telecommunications)
Re: In a trapezium ABCD, AB is parallel to DC, AB = 3DC, and the diagonals  [#permalink]

### Show Tags

03 Aug 2016, 09:24
hsbinfy wrote:
triangles are similar , so ratio will be 1:9

A

AB||DC
A=(base1+base2/2)*h
ratio will change as height changes, no?
Intern
Joined: 11 Jan 2015
Posts: 6
Location: India
GMAT 1: 720 Q50 V38
GPA: 2.9
Re: In a trapezium ABCD, AB is parallel to DC, AB = 3DC, and the diagonals  [#permalink]

### Show Tags

14 Apr 2017, 01:13
1
3
inshor

In Triangle AOB and Triangle COD
Angle AOB = Angle COD (Vertical Angles)
Other two angles are formed between a pair of parallel line AB || DC
Angle BAO = Angle DCO (Alternate interior angle)
Angle ABO = Angle CDO (Alternate interior angle)

Therefore, by AAA Property the two triangle are similar

The ratio of a side is already given, i.e. 1:3

The ratio of their areas will be square of the ratio of their sides (Property of similar triangles)
Ans - 1^2 : 3^2 = 1:9
Non-Human User
Joined: 09 Sep 2013
Posts: 9843
Re: in a trapezium ABCD , AB is parallel to DC , AB = 3DC , and  [#permalink]

### Show Tags

29 Jan 2019, 04:31
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: in a trapezium ABCD , AB is parallel to DC , AB = 3DC , and   [#permalink] 29 Jan 2019, 04:31
Display posts from previous: Sort by