Is the quadrilateral ABCD a square?

Question

(1) All four sides of ABCD have the same length.
(2) Two of the adjacent angles of ABCD add up to 180 degrees.

reto · Answer

Statement 1, tells us that ABCD can be a Square OR a rhombus. Therefore IS.
Statement 2, tells us nothing new about what we already know about any quadrilateral. Adjacent angles add up to 180. This can be a Rhombus or Square.

Answer E.

VenoMfTw · Answer

Statement 1: All four sides of ABCD have the same length. 
ABCD can be a square or rhombus.
 Hence not suff

Statement 2: Two of the adjacent angles of ABCD add up to 180 degrees. 
It tells us that ABCD is a quadrilateral. 
 Hence not suff

Combined:  
Even square and rhombus has their adj angles sum = 180. 
 Hence not suff

GMATinsight · Answer

Question : Is the quadrilateral ABCD a square?

Statement 1 : All four sides of ABCD have the same length. 
i.e. Quadrilateral can be a Square or a Rhombus. Hence,
 NOT SUFFICIENT

Statement 2 : Two of the adjacent angles of ABCD add up to 180 degrees. 
i.e. Quadrilateral can be a Square or a Rhombus or a parallelogram of a Rectangle. Hence,
 NOT SUFFICIENT

Combining the two statements  
i.e. Quadrilateral can be a Square or a Rhombus. Hence,
 NOT SUFFICIENT

Answer : Option E.

jayanthjanardhan · Answer

isnt rhombus a type of square?...so should'nt the answer be 'A'?

GMATinsight · Answer

Square is type of Rhombus

BUT

Rhombus is NOT a type of square

longfellow · Answer

E

1. it could be rhombus or square
2. could be rhombus or square

both are not sufficient

Bunuel · Answer

800score Official Solution:

It is important that you're not fooled by questions like these. On the surface of statement (1), it would immediately seem that a quadrilateral with four sides of equal length would be a square. Remember, however, that this property also applies to a rhombus. Statement (1) is therefore insufficient. Statement (2) is also insufficient. All parallelograms have this property. Taken together, both statements are still insufficient. The quadrilateral could still be either a rhombus or a square.  The answer is (E) .

Bunuel · Answer

Ashishsteag · Answer

I am having slight confusion in statement 1,All squares are both rhombus and rectangles.That's what I read in GMAT mathclub book. So,if a square is also a rhombus.Then,the answer to the question:is the quadrilateral ABCD a square? would be "NO".Isn't it? So the answer should be A. What am i missing here?

abhimahna · Answer

All squares are rhombus and rectangle but the converse is not true. I mean a rectangle or a rhombus may or may not be a square.

So, A tells us that ABCD is a square or a rhombus. Hence, if we could have ABCD a rhombus, in that case it may or may not be a square.

Nunuboy1994 · Answer

They key concepts in this question are that all squares are rhombuses but not all rhombuses are squares. A rhombus has both four equal sides AND two adjacent angles of ABCD add up to 180. ALSO if a four sided figure's diagonals are perpendicular bisectors then the figure   must   be a rhombus.

E

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Is the quadrilateral ABCD a square?

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Is the quadrilateral ABCD a square?

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