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# Is the quadrilateral ABCD a square?

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Math Expert
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29 Jul 2015, 03:09
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59% (00:44) correct 41% (00:42) wrong based on 352 sessions

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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.

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29 Jul 2015, 03:29
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1
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.

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29 Jul 2015, 08:56
2
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.

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

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30 Jul 2015, 03:35
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jayanthjanardhan wrote:
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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Updated on: 31 Jul 2015, 01:51
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: 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
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Originally posted by VenoMfTw on 29 Jul 2015, 03:53.
Last edited by VenoMfTw on 31 Jul 2015, 01:51, edited 1 time in total.
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30 Jul 2015, 03:16
isnt rhombus a type of square?...so should'nt the answer be 'A'?
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30 Jul 2015, 05:37
E

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

both are not sufficient
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17 Aug 2015, 09:04
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.

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).
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17 Aug 2015, 09:08
Bunuel 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.

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).

Similar questions to practice:
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is-abcd-rectangular-156356.html
is-abcd-a-rombus-1-abcd-is-a-square-2-abcd-diagonals-bisect-97819.html

Hope it helps.
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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.

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?
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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.

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.
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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.

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24 Sep 2018, 20:49
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Re: Is the quadrilateral ABCD a square?   [#permalink] 24 Sep 2018, 20:49
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