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

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Math Expert
Joined: 02 Sep 2009
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Is quadrilateral ABCD a square? (1) AB = BC = CD = DA (2) x + y = 180  [#permalink]

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12 Nov 2017, 23:12
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Question Stats:

65% (00:33) correct 35% (00:34) wrong based on 199 sessions

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(1) AB = BC = CD = DA

(2) x + y = 180

Attachment:

20120326021046767_3601.jpg [ 3.45 KiB | Viewed 4495 times ]

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Joined: 05 Dec 2016
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GMAT 1: 620 Q46 V29
Re: Is quadrilateral ABCD a square? (1) AB = BC = CD = DA (2) x + y = 180  [#permalink]

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12 Nov 2017, 23:20
1
(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

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

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14 Nov 2017, 06:35
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.
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Re: Is quadrilateral ABCD a square? (1) AB = BC = CD = DA (2) x + y = 180  [#permalink]

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14 Nov 2017, 07:15
Bunuel wrote:

(1) AB = BC = CD = DA

(2) x + y = 180

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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16 Nov 2017, 22:09
Bunuel wrote:

(1) AB = BC = CD = DA

(2) x + y = 180

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.

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]

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25 Jun 2019, 07:15
From (1) It can be a rhombus or square, hence NS (BCE can be the ans)
From (2) x+y=180 ( multiple values of x and y can satisfy this), hence NS (CE can be the ans)

From (1) & (2); we cannot conclude that any of the angle is a right angle, even when all sides are equal and hence E.
Re: Is quadrilateral ABCD a square? (1) AB = BC = CD = DA (2) x + y = 180   [#permalink] 25 Jun 2019, 07:15