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.
rhombus ds mgmat
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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
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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 .
If you know our own innovative logics to find the answer, you don't need to actually solve the problem.
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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 .
If you know our own innovative logics to find the answer, you don't need to actually solve the problem.
www.mathrevolution.com
- The one-and-only World's First Variable Approach for DS and IVY Approach for PS that allow anyone to easily solve GMAT math questions.
- The easy-to-use solutions. Math skills are totally irrelevant. Forget conventional ways of solving math questions.
- The most effective time management for GMAT math to date allowing you to solve 37 questions with 10 minutes to spare
- Hitting a score of 45 is very easy and points and 49-51 is also doable.
- Unlimited Access to over 120 free video lessons at https://www.mathrevolution.com/gmat/lesson
- Our advertising video at https://www.youtube.com/watch?v=R_Fki3_2vO8
Last edited by Max@Math Revolution on Sun Sep 06, 2015 10:38 pm, edited 1 time in total.
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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 ∠BCD=60, and the angles inside ∆BCD must sum to 180, ∠CBD + ∠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 ∆BCD, since CB=CD, ∠CBD = ∠CDB.
Since ∠CBD = ∠CDB, and ∠CBD + ∠CDB = 120, ∠CBD = ∠CDB = 60.
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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 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.