in a rhombus sides are congruent (equal), diagonals are perpendicular
Is ABDE a rhombus-? for ABDE to be rhombus, the following conditions must be met AB=BD=DE=AE and AD perpendicular to BE.
st(1) \_BCD=60`, hence \_ADE=60` because of parallelism BC||AD. ABC=(180-60)`=120` and ABC=ADC. ABD=120`/2=60` and BDE=60+60=120`. Now if \_BDE=\_BAE, then ew have congruent sides BD=AE=AB=DE because triangles ABD=ADE are equilateral {ABD=120`/2=60` perpendicular diagonals dividing angles by 2 and forming 60-60-60` triangles}, BUT we don't know if \_BDE=\_BAE, Not Sufficient alone.
st(2) Not sufficient alone, as we don't know if all sides are congruent;
Combined st(1&2): must be sufficient as the sides are congruent.
IOM c
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Rhombus - MGMAT
Source: Beat The GMAT — Data Sufficiency |
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Statement 1: BCD = 60 degreesQuadrilateral 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
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.
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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].
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Thanks GMATGuruNY for explaining it so well! You got a knack for simplifying problems. The solution makes sense now. I had gone with B but i understand my mistake now.GMATGuruNY wrote:
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.
OA is C.
