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manhattan rhombus

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


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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
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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.

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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
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by arora007 » Sun Feb 13, 2011 10:39 pm
vaflaly , perfect!! C is the choice!
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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
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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.

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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.

Image
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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.

Image
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
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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.

Image
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
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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
Image
Statement 1: BCD = 60 degrees
In the figure below, ABDE is a rhombus:
Image
In the figure below, ABDE is not a rhombus:
Image
Insufficient.

Statement 2: AE||BD
In the figure below, ABDE is a rhombus:
Image
In the figure below, ABDE is not a rhombus:
Image
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:
Image
Sufficient.

The correct answer is C.
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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?
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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.
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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.
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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.
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