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Is Quadrilateral ABCD a Rhombus? 1) Diagonals of ABCD intersect each

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GMATinsight
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Is Quadrilateral ABCD a Rhombus? 1) Diagonals of ABCD intersect each [#permalink] New post   07 May 2017, 21:14
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Is Quadrilateral ABCD a Rhombus?

1) Diagonals of ABCD Bisect each other at 90 degrees
2) Diagonals of ABCD are equal in dimension

Source: https://www.GMATInsight.com
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Re: Is Quadrilateral ABCD a Rhombus? 1) Diagonals of ABCD intersect each [#permalink] New post   07 May 2017, 21:20
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GMATinsight wrote:
Is Quadrilateral ABCD a Rhombus?

1) Diagonals of ABCD Bisect each other at 90 degrees
2) Diagonals of ABCD are equal in dimension

Source: https://www.GMATInsight.com


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Re: Is Quadrilateral ABCD a Rhombus? 1) Diagonals of ABCD intersect each [#permalink] New post   Updated on: 07 May 2017, 22:51
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1. If the diagonals bisect each other, the quadilateral is a rhombus. Hence sufficient.

2. If the diagonals are equal, the quadilateral could be a square or rectangle. A square is a rhombus with each of its interior angles = 90degree. Hence, insufficient as it could either be a sqaure or a rectangle.
(Option A)

Originally posted by pushpitkc on 07 May 2017, 21:28.
Last edited by pushpitkc on 07 May 2017, 22:51, edited 1 time in total.
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Re: Is Quadrilateral ABCD a Rhombus? 1) Diagonals of ABCD intersect each [#permalink] New post   07 May 2017, 21:57
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Statement 1. In a quadrilateral, if diagonals bisect each other at 90 degrees, it must be a Rhombus (well we can say that it happens in a square also but then every square is a rhombus, its a special kind of rhombus). Sufficient.

Statement 2. Diagonals of quadrilateral are equal. It could be a rectangle or a square or an isosceles trapezoid. If its a square, then we can call it a rhombus (square is a special kind of rhombus) but in other two cases, we cannot call it a rhombus. Insufficient.

Hence A.
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Re: Is Quadrilateral ABCD a Rhombus? 1) Diagonals of ABCD intersect each [#permalink] New post   08 May 2017, 07:47
Statement 1. In a quadrilateral, if diagonals bisect each other at 90 degrees, it must be a Rhombus... Suff

Statement 2. Diagonals of quadrilateral are equal. It could be a rectangle or a square... Insuff

Hence A.
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Re: Is Quadrilateral ABCD a Rhombus? 1) Diagonals of ABCD intersect each [#permalink] New post   08 May 2017, 22:48
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GMATinsight wrote:
Is Quadrilateral ABCD a Rhombus?

1) Diagonals of ABCD Bisect each other at 90 degrees
2) Diagonals of ABCD are equal in dimension

Source: https://www.GMATInsight.com

Good question. The word BISECT should not be ignored.

Diagonals of Quadrilateral intersect each other at 90 degrees: Quadrilateral can be Rhombus or Kite.
Diagonals of Quadrilateral Bisect each other at 90 degrees: Quadrilateral is definitely a Rhombus! Hence, Statement-1 is sufficient.

Diagonals of Quadrilateral are equal in dimension: Quadrilateral can be Square (note that Square is a Rhombus with each interior angle as 90 degrees) or Rectangle or a Trapezium with equal non-parallel sides. Hence, Statement-2 is insufficient.

Answer: A.
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Re: Is Quadrilateral ABCD a Rhombus? 1) Diagonals of ABCD intersect each [#permalink] New post   10 Sep 2017, 11:52
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pushpitkc wrote:
1. If the diagonals bisect each other, the quadilateral is a rhombus. Hence sufficient.

2. If the diagonals are equal, the quadilateral could be a square or rectangle. A square is a rhombus with each of its interior angles = 90degree. Hence, insufficient as it could either be a sqaure or a rectangle.
(Option A)


Is the word bisect and intersect same?
If it is not same then it could be kite also. In that case A is not the answer.

Bunuel / Experts please help.
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Re: Is Quadrilateral ABCD a Rhombus? 1) Diagonals of ABCD intersect each [#permalink] New post   10 Sep 2017, 12:12
To bisect a line means to divide the line into two equal halves.

But if a line Intersects another line at Point X, it means that the point at which the two lines meet is point X. It doesn't mean that the lines is divided into equal halves
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Re: Is Quadrilateral ABCD a Rhombus? 1) Diagonals of ABCD intersect each [#permalink] New post   20 Feb 2019, 23:07
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GMATinsight wrote:
Is Quadrilateral ABCD a Rhombus?

1) Diagonals of ABCD Bisect each other at 90 degrees
2) Diagonals of ABCD are equal in dimension

Source: https://www.GMATInsight.com


Question: Is Quadrilateral ABCD a Rhombus?

Properties of Rhombus:
1) All sides of the quadrilateral are equal (Ensuring property)
2) Diagonals are not essentially equal
3) Diagonals bisect (divide each other equally) each other @90º (Ensuring Property)
4) Diagonally Opposite angles of quadrilateral are equal
5) Square is a type of Rhombus

Statement 1: Diagonals of ABCD Bisect each other at 90 degrees

Property 3 ensures that it is a Rhombus hence

SUFFICIENT

Statement 2: Diagonals of ABCD are equal in dimension

The quadrilateral may be a rectangle (not a rhombus) or square (a rhombus) hence

NOT SUFFICIENT

Answer: Option A
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Re: Is Quadrilateral ABCD a Rhombus? 1) Diagonals of ABCD intersect each [#permalink] New post   07 Jun 2023, 20:36
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Re: Is Quadrilateral ABCD a Rhombus? 1) Diagonals of ABCD intersect each [#permalink]
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