manhattan rhombus

Expert replies

arora007: Community Manager; Posts: 1048; Joined: Mon Aug 17, 2009 3:26 amFollowed by: 27 members; Location: India; Thanked: 51 times; GMAT Score:670

by arora007 » Sun Feb 13, 2011 7:50 am

Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?

(1) The measure of angle BCD is 60 degrees.
(2) AE is parallel to BD

https://www.skiponemeal.org/
https://twitter.com/skiponemeal
Few things are impossible to diligence & skill.Great works are performed not by strength,but by perseverance

pm me if you find junk/spam/abusive language, Lets keep our community clean!!

Like this post

Source: Beat The GMAT — Data Sufficiency | Sun Feb 13, 2011 7:50 am

Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Sun Feb 13, 2011 8:44 am

arora007 wrote:Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?

(1) The measure of angle BCD is 60 degrees.
(2) AE is parallel to BD

IOM B actually

st(1) Is not sufficient as it tells us only angl.ABD=60`, angl.BDE=120 and no data about the line segments DE, AE
st(2) Sufficient as AE//BD, since E is on line segment CD-E, DE//AB, angl.AED=angl.ABD, angl.BAE=angl.BDE, ABDE is rhombus

Attachments

Like this post

maihuna: Legendary Member; Posts: 1578; Joined: Sun Dec 28, 2008 1:49 amFollowed by: 9 members; Thanked: 82 times; GMAT Score:720

by maihuna » Sun Feb 13, 2011 8:49 am

Rhombus is a parallelogram where opposite angles are equal, and adjacent complementary..

So we may first prove ABDE parallelogram, and then angle req.

A: Knowing measure of C only tells BAD=60 and ABC=ADC=120. not suff

B: it means ABDE is a parallelogram. Not suff.

combine:

Charged up again to beat the beast

Like this post

vaflaly: Junior | Next Rank: 30 Posts; Posts: 27; Joined: Thu Oct 21, 2010 8:40 am

by vaflaly » Sun Feb 13, 2011 11:30 am

a rhombus is a parallelogram with four equal sides

(1) ---> BCD is 60 deg, but No info about position of E,

INSUFF

(2)----> BE // AB and DB//AE
so ABDE is a parallelogram; but we dont know wheter BD=AE=AB=DE

INSUFF

(1)&(2);

BCD=60 and BC=CD so triangle BCD is equilateral ---> BD=CD=AB

ABDE parallelogram ---> BD=AE and AB=DE

so BD=AE=AB=DE

Suffi

Answer is C

Like this post

arora007: Community Manager; Posts: 1048; Joined: Mon Aug 17, 2009 3:26 amFollowed by: 27 members; Location: India; Thanked: 51 times; GMAT Score:670

by arora007 » Sun Feb 13, 2011 10:39 pm

vaflaly , perfect!! C is the choice!

Like this post

Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Mon Feb 14, 2011 7:38 am

@arora: what's the source of this question?
Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?

(1) The measure of angle BCD is 60 degrees.
(2) AE is parallel to BD

statement (2) AE//BD, since E is on line segment CD-E --> DE//AB. AE and AB share the same point in A, therefore AE=BD, AB=ED, and the angle relationship is remained the same. Sufficient.

statement (1) angl.BCD=60` is Not Sufficient

Answer C involves the angle 60` (BCD). We already know that the angle relationship is remained, so A is not necessary.

vaflaly wrote:a rhombus is a parallelogram with four equal sides

(1) ---> BCD is 60 deg, but No info about position of E,

INSUFF

(2)----> BE // AB and DB//AE
so ABDE is a parallelogram; but we dont know wheter BD=AE=AB=DE

INSUFF

(1)&(2);

BCD=60 and BC=CD so triangle BCD is equilateral ---> BD=CD=AB

ABDE parallelogram ---> BD=AE and AB=DE

so BD=AE=AB=DE

Suffi

Answer is C

Like this post

arora007: Community Manager; Posts: 1048; Joined: Mon Aug 17, 2009 3:26 amFollowed by: 27 members; Location: India; Thanked: 51 times; GMAT Score:670

by arora007 » Mon Feb 14, 2011 8:45 am

This wonderful problem is from Manhattan test (#3)

Yaa.. C is the answer... tried to draw a rough sketch.

Like this post

Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Mon Feb 14, 2011 9:21 am

are not points C, D, and E on the same line? Moreover ABCD is a rhombus.

arora007 wrote:This wonderful problem is from Manhattan test (#3)

Yaa.. C is the answer... tried to draw a rough sketch.

Like this post

arora007: Community Manager; Posts: 1048; Joined: Mon Aug 17, 2009 3:26 amFollowed by: 27 members; Location: India; Thanked: 51 times; GMAT Score:670

by arora007 » Mon Feb 14, 2011 1:19 pm

Night reader wrote:are not points C, D, and E on the same line? Moreover ABCD is a rhombus.

arora007 wrote:This wonderful problem is from Manhattan test (#3)

Yaa.. C is the answer... tried to draw a rough sketch.

I told its a rough image... a very rough image...

C-D-E are on the same line....

ABCD is a rhombus, but the point is... in my case the angle BCD is about 40 degrees and ABDE is not a rhombus

Like this post

Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Mon Feb 14, 2011 1:44 pm

OK, I just realized without st(1) there's no way for us to prove that all sides of the quadrilateral ABDE are equal, and we have rhombus. It should be C.

arora007 wrote:
Night reader wrote:are not points C, D, and E on the same line? Moreover ABCD is a rhombus.

arora007 wrote:This wonderful problem is from Manhattan test (#3)

Yaa.. C is the answer... tried to draw a rough sketch.

I told its a rough image... a very rough image...

C-D-E are on the same line....

ABCD is a rhombus, but the point is... in my case the angle BCD is about 40 degrees and ABDE is not a rhombus

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Feb 14, 2011 3:00 pm

arora007 wrote:Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?

(1) The measure of angle BCD is 60 degrees.
(2) AE is parallel to BD

Statement 1: BCD = 60 degrees
In the figure below, ABDE is a rhombus:

In the figure below, ABDE is not a rhombus:

Insufficient.

Statement 2: AE||BD
In the figure below, ABDE is a rhombus:

In the figure below, ABDE is not a rhombus:

Insufficient.

Statements 1 and 2 together:
If BCD is 60 degrees, and AE||BD, then all the angles shown must be 60 degrees, all the triangles shown must be equilateral, and ABDE must be a rhombus:

Sufficient.

The correct answer is C.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

JayLow: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Wed Feb 16, 2011 11:41 am

by JayLow » Wed Feb 16, 2011 11:51 am

I can't visualize this except to give B as an answer can anyone show a pic where ABDE is not a rhombus?

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Feb 16, 2011 11:57 am

JayLow wrote:I can't visualize this except to give B as an answer can anyone show a pic where ABDE is not a rhombus?

My explanation above offers pictures that show why neither statement is sufficient on its own. Included is a figure that satisfies the conditions given in Statement 2 and in which ABDE is not a rhombus.

Like this post

JayLow: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Wed Feb 16, 2011 11:41 am

by JayLow » Wed Feb 16, 2011 12:28 pm

GMATGuruNY wrote:
JayLow wrote:I can't visualize this except to give B as an answer can anyone show a pic where ABDE is not a rhombus?
My explanation above offers pictures that show why neither statement is sufficient on its own. Included is a figure that satisfies the conditions given in Statement 2 and in which ABDE is not a rhombus.

I'm afraid they don't appear.

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Feb 16, 2011 12:41 pm

JayLow wrote:
GMATGuruNY wrote:
JayLow wrote:I can't visualize this except to give B as an answer can anyone show a pic where ABDE is not a rhombus?
My explanation above offers pictures that show why neither statement is sufficient on its own. Included is a figure that satisfies the conditions given in Statement 2 and in which ABDE is not a rhombus.
I'm afraid they don't appear.

Here's a .pdf of the drawings.

Attachments

Rhombus problem.pdf: (87.61 KiB) Downloaded 99 times

Like this post

Post new topic Post Reply

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review