rhombus ds mgmat

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rommysingh: Master | Next Rank: 500 Posts; Posts: 112; Joined: Thu Mar 22, 2012 9:33 amFollowed by: 1 member; Thanked: 1 times

by rommysingh » Fri Sep 04, 2015 1:23 pm

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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Source: Beat The GMAT — Data Sufficiency | Fri Sep 04, 2015 1:23 pm

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 » Fri Sep 04, 2015 4:38 pm

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.

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Sun Sep 06, 2015 7:39 pm

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.

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.

transforming the original condition by variable approach method, we have 2 variables for the rhombus (side length and one diagonal side length). Since we need to match the number of variables and equations, we need 2 more equations. Since there is 1 equation each in 1) and 2), C is likely the answer and it turns out that C actually is the answer .

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Last edited by Max@Math Revolution on Sun Sep 06, 2015 10:38 pm, edited 1 time in total.

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sandipgumtya: Master | Next Rank: 500 Posts; Posts: 126; Joined: Sat Jun 07, 2014 5:26 am; Thanked: 3 times

by sandipgumtya » Sun Sep 06, 2015 7:45 pm

Hi Mitch,
I didn't get how r u getting angle CBD=CDB=60DEG.Can u pl explain once more?

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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 » Tue Sep 08, 2015 10:39 am

sandipgumtya wrote:Hi Mitch,
I didn't get how r u getting angle CBD=CDB=60DEG.Can u pl explain once more?

Angles inside a triangle must sum to 180.
Since statement 1 indicates that âˆ BCD=60, and the angles inside âˆ†BCD must sum to 180, âˆ CBD + âˆ CDB = 120.

The prompt indicates that ABCD is a rhombus.
In a rhombus, all sides are EQUAL.
Thus, CB=CD.

If two sides of a triangle are equal, the opposite angles are also equal.
In âˆ†BCD, since CB=CD, âˆ CBD = âˆ CDB.

Since âˆ CBD = âˆ CDB, and âˆ CBD + âˆ CDB = 120, âˆ CBD = âˆ CDB = 60.

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sandipgumtya: Master | Next Rank: 500 Posts; Posts: 126; Joined: Sat Jun 07, 2014 5:26 am; Thanked: 3 times

by sandipgumtya » Wed Sep 09, 2015 9:29 am

thanks mitch,got it.but what r the essential and sufficient conditions for a quadrilateral to be a rhombus?i didn't get the two figs in statement 2.

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