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Is Quadrilateral ABCD a Rectangle? 1) Diagonals of ABCD Bisect each o  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 44% (00:48) correct 56% (00:42) wrong based on 221 sessions

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

Source: http://www.GMATInsight.com

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Math Expert V
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Posts: 56272
Re: Is Quadrilateral ABCD a Rectangle? 1) Diagonals of ABCD Bisect each o  [#permalink]

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Math Expert V
Joined: 02 Aug 2009
Posts: 7764
Re: Is Quadrilateral ABCD a Rectangle? 1) Diagonals of ABCD Bisect each o  [#permalink]

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GMATinsight wrote:

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

Source: http://www.GMATInsight.com

Main statement tells us that ABCD is a Quadrilateral..

Let's see the statements..

1) Diagonals of ABCD Bisect each other at 90 degrees
this tells us that the diagonals cut each other at middle of each other at 90°
The diagonals can be of different sizes..
So it is surely a RHOMBUS but cannot say if it is rectangle/square

Insufficient

2) Diagonals of ABCD are equal in dimension
Diagonals are equal cannot alone suffice if it's a rectangle..

Combined..
It is a rhombus from statement I and diagonals are EQUAL from statement II..
It is a square and each square is also a rectangle..
Sufficient
C
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Re: Is Quadrilateral ABCD a Rectangle? 1) Diagonals of ABCD Bisect each o  [#permalink]

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chetan2u wrote:
GMATinsight wrote:

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

Source: http://www.GMATInsight.com

Main statement tells us that ABCD is a Quadrilateral..

Let's see the statements..

1) Diagonals of ABCD Bisect each other at 90 degrees
this tells us that the diagonals cut each other at middle of each other at 90°
The diagonals can be of different sizes..
So it is surely a RHOMBUS but cannot say if it is rectangle/square

Insufficient

2) Diagonals of ABCD are equal in dimension
Diagonals are equal cannot alone suffice if it's a rectangle..

Combined..
It is a rhombus from statement I and diagonals are EQUAL from statement II..
It is a square and each square is also a rectangle..
Sufficient
C

Hello chetan2u / Bunuel,
How do we distinguish when to treat a square as A SQUARE and not a rectangle.
It's true all squares are rectangles. I did reach at the conclusion that from both A and B the quadrilateral is a square. But marked "E".
Regards
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Re: Is Quadrilateral ABCD a Rectangle? 1) Diagonals of ABCD Bisect each o  [#permalink]

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hi chetan2u ...

stat2 states diagnols are equal...in a quadrialteral, only square and rectangle have equal diagnols,,,
i cant think of any other figure where diagnols ar equal
Math Expert V
Joined: 02 Aug 2009
Posts: 7764
Re: Is Quadrilateral ABCD a Rectangle? 1) Diagonals of ABCD Bisect each o  [#permalink]

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1
mohshu wrote:
hi chetan2u ...

stat2 states diagnols are equal...in a quadrialteral, only square and rectangle have equal diagnols,,,
i cant think of any other figure where diagnols ar equal

Hi,

Surely if diagonals are EQUAL and BISECT each other, it would be rectangle or square..
But here it is just diagonals are EQUAL. Say both are 5 m but they bisect at 1 m from top, it will not be rectangle or square..
Once you draw, you will see various Quadrilateral can be made .
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GRE 1: Q169 V154 Is Quadrilateral ABCD a Rectangle? 1) Diagonals of ABCD Bisect each o  [#permalink]

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1
mohshu wrote:
hi chetan2u ...

stat2 states diagnols are equal...in a quadrialteral, only square and rectangle have equal diagnols,,,
i cant think of any other figure where diagnols ar equal

Here is an example -->

Check out this trapezoid with equal diagonals It clearly isn't a rectangle
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Re: Is Quadrilateral ABCD a Rectangle? 1) Diagonals of ABCD Bisect each o  [#permalink]

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chetan2u wrote:
mohshu wrote:
hi chetan2u ...

stat2 states diagnols are equal...in a quadrialteral, only square and rectangle have equal diagnols,,,
i cant think of any other figure where diagnols ar equal

Hi,

Surely if diagonals are EQUAL and BISECT each other, it would be rectangle or square..
But here it is just diagonals are EQUAL. Say both are 5 m but they bisect at 1 m from top, it will not be rectangle or square..
Once you draw, you will see various Quadrilateral can be made .

ok..makes sense now,,,,thanks

i guess that shud be intersect??? bisect means dividing each other into two equal parts...
correct me if im rong,,
thanks
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Re: Is Quadrilateral ABCD a Rectangle? 1) Diagonals of ABCD Bisect each o  [#permalink]

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chetan2u wrote:
GMATinsight wrote:

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

Source: http://www.GMATInsight.com

Main statement tells us that ABCD is a Quadrilateral..

Let's see the statements..

1) Diagonals of ABCD Bisect each other at 90 degrees
this tells us that the diagonals cut each other at middle of each other at 90°
The diagonals can be of different sizes..
So it is surely a RHOMBUS but cannot say if it is rectangle/square

Insufficient

2) Diagonals of ABCD are equal in dimension
Diagonals are equal cannot alone suffice if it's a rectangle..

Combined..
It is a rhombus from statement I and diagonals are EQUAL from statement II..
It is a square and each square is also a rectangle..
Sufficient
C

Statement1 is not surely a rhombus. The diagonals of a kite are also perpendicular to each other.

Posted from my mobile device
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Joined: 19 Jul 2017
Posts: 43
Re: Is Quadrilateral ABCD a Rectangle? 1) Diagonals of ABCD Bisect each o  [#permalink]

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MrJglass wrote:
chetan2u wrote:
GMATinsight wrote:

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

Source: http://www.GMATInsight.com

Main statement tells us that ABCD is a Quadrilateral..

Let's see the statements..

1) Diagonals of ABCD Bisect each other at 90 degrees
this tells us that the diagonals cut each other at middle of each other at 90°
The diagonals can be of different sizes..Statement1 is not surely a rhombus. The diagonals of a kite are also perpendicular to each other.

[b]Posted from my mobile device

So it is surely a RHOMBUS but cannot say if it is rectangle/square[/b]
Insufficient

2) Diagonals of ABCD are equal in dimension
Diagonals are equal cannot alone suffice if it's a rectangle..

Combined..
It is a rhombus from statement I and diagonals are EQUAL from statement II..
It is a square and each square is also a rectangle..
Sufficient
C

.

I think there is a difference between "bisect" and "intersect"
In a quadrilateral, if diagonals intersect each other at 90 degrees, then it could be a rhombus or a square or a kite. In first two cases we can call it a rhombus only (because square is a special kind of rhombus) but if its a kite, it cannot be called a rhombus. .
(Please note that the statement does NOT say 'intersect each other at 90' but it says bisect each other at 90'.
Diagonals of a square, a rectangle and an isosceles trapezoid are equal in dimension. In the first case (if its a square) we can call it a rhombus (square is a special kind of rhombus) but in other two cases we cannot.
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Re: Is Quadrilateral ABCD a Rectangle? 1) Diagonals of ABCD Bisect each o  [#permalink]

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chetan2u wrote:
GMATinsight wrote:

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

Source: http://www.GMATInsight.com

Main statement tells us that ABCD is a Quadrilateral..

Let's see the statements..

1) Diagonals of ABCD Bisect each other at 90 degrees
this tells us that the diagonals cut each other at middle of each other at 90°
The diagonals can be of different sizes..
So it is surely a RHOMBUS but cannot say if it is rectangle/square

Insufficient

2) Diagonals of ABCD are equal in dimension
Diagonals are equal cannot alone suffice if it's a rectangle..

Combined..
It is a rhombus from statement I and diagonals are EQUAL from statement II..
It is a square and each square is also a rectangle..
Sufficient
C

Hi chetan2u

Please correct me if I'm wrong. I'm attaching a file with a figure in which diagonals are equal and cross at 90 degree yet the figure is a kite, not a parallelogram.
Attachments 1.png [ 4.88 KiB | Viewed 1264 times ]

Math Expert V
Joined: 02 Aug 2009
Posts: 7764
Re: Is Quadrilateral ABCD a Rectangle? 1) Diagonals of ABCD Bisect each o  [#permalink]

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Hero8888 wrote:
chetan2u wrote:
GMATinsight wrote:

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

Source: http://www.GMATInsight.com

Main statement tells us that ABCD is a Quadrilateral..

Let's see the statements..

1) Diagonals of ABCD Bisect each other at 90 degrees
this tells us that the diagonals cut each other at middle of each other at 90°
The diagonals can be of different sizes..
So it is surely a RHOMBUS but cannot say if it is rectangle/square

Insufficient

2) Diagonals of ABCD are equal in dimension
Diagonals are equal cannot alone suffice if it's a rectangle..

Combined..
It is a rhombus from statement I and diagonals are EQUAL from statement II..
It is a square and each square is also a rectangle..
Sufficient
C

Hi chetan2u

Please correct me if I'm wrong. I'm attaching a file with a figure in which diagonals are equal and cross at 90 degree yet the figure is a kite, not a parallelogram.

Yes, it is not a parallelogram.
The reason is that the diagonals have to be equal and bisect each other and if you do the same here, it will become a rhombus
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Is Quadrilateral ABCD a Rectangle? 1) Diagonals of ABCD Bisect each o  [#permalink]

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chetan2u wrote:
Sufficient
C

Hi chetan2u

Please correct me if I'm wrong. I'm attaching a file with a figure in which diagonals are equal and cross at 90 degree yet the figure is a kite, not a parallelogram.[/quote]

Yes, it is not a parallelogram.
The reason is that the diagonals have to be equal and bisect each other and if you do the same here, it will become a rhombus[/quote]

Sorry, I meant Rectangle. So the OA has to be E?

Originally posted by Hero8888 on 23 Aug 2018, 06:35.
Last edited by Hero8888 on 23 Aug 2018, 07:04, edited 1 time in total.
Math Expert V
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Re: Is Quadrilateral ABCD a Rectangle? 1) Diagonals of ABCD Bisect each o  [#permalink]

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1
Hero8888 wrote:
chetan2u wrote:
Sufficient
C

Hi chetan2u

Please correct me if I'm wrong. I'm attaching a file with a figure in which diagonals are equal and cross at 90 degree yet the figure is a kite, not a parallelogram.

Yes, it is not a parallelogram.
The reason is that the diagonals have to be equal and bisect each other and if you do the same here, it will become a rhombus[/quote]

Sorry, I meant Rectangle. So the OA has to be E.[/quote]

NO, the OA will be C.

you have not read the complete info of statement I.
1) Diagonals of ABCD Bisect each other at 90 degrees
so statement I tells us that the diagonals bisect each other. Bisect means they intersect at the centre.

so combined it has to be a rectangle - equal diagonals and bisecting each other at 90 would be a square and square is also a rectangle
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Re: Is Quadrilateral ABCD a Rectangle? 1) Diagonals of ABCD Bisect each o  [#permalink]

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Why statement 1 alone is not sufficient??
Diagonals of a rectangle do not bisect at 90 deg. So statement 1 should be sufficient to decide that its not a rectangle but any other quadrilateral (may be a square)

Posted from my mobile device
Math Expert V
Joined: 02 Aug 2009
Posts: 7764
Re: Is Quadrilateral ABCD a Rectangle? 1) Diagonals of ABCD Bisect each o  [#permalink]

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ranjitmkunte wrote:
Why statement 1 alone is not sufficient??
Diagonals of a rectangle do not bisect at 90 deg. So statement 1 should be sufficient to decide that its not a rectangle but any other quadrilateral (may be a square)

Posted from my mobile device

A square is always a rectangle, although it may not be necessary that a rectangle is a square.
_________________ Re: Is Quadrilateral ABCD a Rectangle? 1) Diagonals of ABCD Bisect each o   [#permalink] 24 Aug 2018, 07:35
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