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Is quadrilateral ABCD a square? (1) AB = BC = CD = DA (2) x + y = 180

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Is quadrilateral ABCD a square? (1) AB = BC = CD = DA (2) x + y = 180 [#permalink]

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Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA

(2) x + y = 180


[Reveal] Spoiler:
Attachment:
20120326021046767_3601.jpg
20120326021046767_3601.jpg [ 3.45 KiB | Viewed 632 times ]
[Reveal] Spoiler: OA

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Re: Is quadrilateral ABCD a square? (1) AB = BC = CD = DA (2) x + y = 180 [#permalink]

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(1) It can be either rhombus or square, so Insufficient
(2) case 1: x=y=90 hence it is square
case 2: x=50; y 130 hence it is not squre
(1) + (2) It can still be either rhombus or square

Answer E.

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Re: Is quadrilateral ABCD a square? (1) AB = BC = CD = DA (2) x + y = 180 [#permalink]

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New post 14 Nov 2017, 07:35
ST1 All sides are equal, thus it can be either rhombus or square, so Insufficient.
St2 sum of 2 consecutive angle is 180, it is not sufficient. as angles can be of any order
Combining ST1 & ST2 , It can be a square or rhombus.
Answer E.
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Re: Is quadrilateral ABCD a square? (1) AB = BC = CD = DA (2) x + y = 180 [#permalink]

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New post 14 Nov 2017, 08:15
Bunuel wrote:
Image
Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA

(2) x + y = 180


[Reveal] Spoiler:
Attachment:
20120326021046767_3601.jpg


Statement 1: All sides can be equal in a rhombus as well as a square. This statement is insufficient. A square can be a special type of rhombus but vice versa is not true. With this given condition had the question asked if the quadrilateral is a rhombus, then the answer would have been "yes".

Statement 2: Sum of adjacent angles is equal to 180 degrees in a rectangle rhombus and square. Insufficient.

Together also, the quadrilateral can be either a square or rhombus. hence, insufficient. E.

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Re: Is quadrilateral ABCD a square? (1) AB = BC = CD = DA (2) x + y = 180 [#permalink]

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New post 16 Nov 2017, 23:09
Bunuel wrote:
Image
Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA

(2) x + y = 180


[Reveal] Spoiler:
Attachment:
20120326021046767_3601.jpg



Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

A quadrilateral has 5 variables by VA method.

Since we have 3 equations from the condition 1) and we have 1 equation from the condition 2), both conditions together are not sufficient.

E is the answer.

For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80 % chance that E is the answer, while C has 15% chance and A, B or D has 5% chance. Since E is most likely to be the answer using 1) and 2) together according to DS definition. Obviously there may be cases where the answer is A, B, C or D.
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Re: Is quadrilateral ABCD a square? (1) AB = BC = CD = DA (2) x + y = 180   [#permalink] 16 Nov 2017, 23:09
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