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Re: Is the quadrilateral ABCD a square? [#permalink]

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29 Jul 2015, 03:29

1

This post received KUDOS

Bunuel wrote:

Is the quadrilateral ABCD a square?

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

Kudos for a correct solution.

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.
_________________

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

Kudos for a correct solution.

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

Square is type of Rhombus

BUT

Rhombus is NOT a type of square _________________

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

Kudos for a correct solution.

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).
_________________

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

Kudos for a correct solution.

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).

Re: Is the quadrilateral ABCD a square? [#permalink]

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02 Sep 2016, 01:47

reto wrote:

Bunuel wrote:

Is the quadrilateral ABCD a square?

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

Kudos for a correct solution.

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.

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?

Re: Is the quadrilateral ABCD a square? [#permalink]

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04 Sep 2016, 00:53

Ashishsteag wrote:

reto wrote:

Bunuel wrote:

Is the quadrilateral ABCD a square?

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

Kudos for a correct solution.

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.

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?

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.
_________________

Re: Is the quadrilateral ABCD a square? [#permalink]

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06 Sep 2017, 23:05

Bunuel wrote:

Is the quadrilateral ABCD a square?

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

Kudos for a correct solution.

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.