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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Is quadrilateral ABCD a square? (1) AB = BC = CD = DA (2) x + y = 180

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Math Expert V
Joined: 02 Sep 2009
Posts: 59588
Is quadrilateral ABCD a square? (1) AB = BC = CD = DA (2) x + y = 180  [#permalink]

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1
6 00:00

Difficulty:   15% (low)

Question Stats: 64% (00:34) correct 36% (00:34) wrong based on 177 sessions

### HideShow timer Statistics (1) AB = BC = CD = DA

(2) x + y = 180

Attachment: 20120326021046767_3601.jpg [ 3.45 KiB | Viewed 3948 times ]

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Manager  S
Joined: 05 Dec 2016
Posts: 232
Concentration: Strategy, Finance
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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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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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.
Manager  B
Joined: 11 Jun 2017
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Re: Is quadrilateral ABCD a square? (1) AB = BC = CD = DA (2) x + y = 180  [#permalink]

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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.
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8235
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Is quadrilateral ABCD a square? (1) AB = BC = CD = DA (2) x + y = 180  [#permalink]

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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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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, 08:15
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# Is quadrilateral ABCD a square? (1) AB = BC = CD = DA (2) x + y = 180  