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Is quadrilateral ABCD a rectangle?

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BrentGMATPrepNow
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Is quadrilateral ABCD a rectangle? [#permalink] New post   29 Nov 2016, 07:30
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Is quadrilateral ABCD a rectangle?

(1) The diagonals (AC and BD) are perpendicular to each other
(2) The sum of any 3 angles in the quadrilateral is 270 degrees

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Re: Is quadrilateral ABCD a rectangle? [#permalink] New post   30 Apr 2018, 13:40
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goalMBA1990 wrote:
I have a query for statement 2. We are told that sum of any 3 angles is 270. So how can we assume that each will be 90? It can be any value. So ans should be E. What am I missing?


(2) The sum of any 3 angles in the quadrilateral is 270 degrees
The key word here is ANY.
Let's call the 4 angles a, b, c and d
If ANY 3 angles add to 270, we can write 4 possible equations.
a + b + c = 270. This means that angle d MUST EQUAL 90 degrees (since all 4 angles must add to 360 degrees)
a + b + d = 270. This means that angle c MUST EQUAL 90 degrees (since all 4 angles must add to 360 degrees)
a + c + d = 270. This means that angle b MUST EQUAL 90 degrees (since all 4 angles must add to 360 degrees)
b + c + d = 270. This means that angle a MUST EQUAL 90 degrees (since all 4 angles must add to 360 degrees)
At this point, we shown that all 4 angles must equal 90 degrees.

Cheers,
Brent
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Re: Is quadrilateral ABCD a rectangle? [#permalink] New post   29 Nov 2016, 10:25
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vikrantsharma725@gmail.com wrote:
A is clear that quadrilateral can be rhombus as diagonals of rhombus are also prependicular.

but why answer is B. as it can be square also since it is given in B that sum of any 3 sides is 270 degree. and it can be rectangle also. but if we combine B and A then diagonals of rectangle are prependicular and sum of 3 sides is also 270 degree.

so please tell me why not answer is C


Great question! In fact, it illustrates why I created the question in the first place.

A square is a type of rectangle. So, if the quadrilateral is a square, then we can also conclude that the quadrilateral is a rectangle.

From the Official Guide:
A parallelogram with right angles is a rectangle, and a rectangle with all sides of equal length is a square.

For more on this, here's a video:
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Re: Is quadrilateral ABCD a rectangle? [#permalink] New post   29 Nov 2016, 07:40
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GMATPrepNow wrote:
Is quadrilateral ABCD a rectangle?

(1) The diagonals (AC and BD) are perpendicular to each other
(2) The sum of any 3 angles in the quadrilateral is 270 degrees

*Kudos for all correct solutions


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Re: Is quadrilateral ABCD a rectangle? [#permalink] New post   29 Nov 2016, 08:44
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Omkar.kamat wrote:
Omkar.kamat wrote:
nguyendinhtuong wrote:
Is quadrilateral ABCD a rectangle?

(1) The diagonals (AC and BD) are perpendicular to each other
(2) The sum of any 3 angles in the quadrilateral is 270 degrees

(1) Insufficient. The diagonals of a rectangle could be perpendicular to each other (then it's a square) or not.
(2) The sum of 4 angles in the quadrilateral is 360. Hence, any of 4 angles in the quadrilater is 90 degree. So ABCD is a rectangle.

The answer is B.

Please re look... When diagonals are parallel...it's a Rhombus...not a Rectangle.

Answer shud be A. If the diagonals are perpendicular it's not a Rectangle.sufficient.

B is not sufficient, as the sum doesn't give any clarity about which figure it is.

Correct me if wrong.


Sorry. I meant perpendicular.

Omkar Kamat
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Here is why A is insufficient
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Re: Is quadrilateral ABCD a rectangle? [#permalink] New post   29 Nov 2016, 18:42
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vikrantsharma725@gmail.com wrote:
A is clear that quadrilateral can be rhombus as diagonals of rhombus are also prependicular.

but why answer is B. as it can be square also since it is given in B that sum of any 3 sides is 270 degree. and it can be rectangle also. but if we combine B and A then diagonals of rectangle are prependicular and sum of 3 sides is also 270 degree.

so please tell me why not answer is C


The answer is not C because we need only B enough to deduce that ABCD is a rectangle.

(1) is insufficient due to #7.

Let me make clearer in (1). If diagonals of ABCD are prependicular, ABCD could be a rhombus or not.
If ABCD is a rhombus, it could be a square or not.
If ABCD is a square, it's also a rectangle.

So (1) => ABCD could be a rectangle or not. Insufficient.

(2) A quadrilateral with 4 right angles is a rectangle. If ABCD is a square, it's clearly a rectangle since square is a special type of rectangle. In all cases, we have ABCD is a rectangle. So (2) is sufficient to answer the question.

Hope this helps.
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Re: Is quadrilateral ABCD a rectangle? [#permalink] New post   29 Nov 2016, 08:11
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GMATPrepNow wrote:
Is quadrilateral ABCD a rectangle?

(1) The diagonals (AC and BD) are perpendicular to each other
(2) The sum of any 3 angles in the quadrilateral is 270 degrees


(1) Insufficient. The diagonals of a rectangle could be perpendicular to each other (then it's a square) or not.
(2) The sum of 4 angles in the quadrilateral is 360. Hence, any of 4 angles in the quadrilater is 90 degree. So ABCD is a rectangle.

The answer is B.
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Re: Is quadrilateral ABCD a rectangle? [#permalink] New post   29 Nov 2016, 08:23
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nguyendinhtuong wrote:
GMATPrepNow wrote:
Is quadrilateral ABCD a rectangle?

(1) The diagonals (AC and BD) are perpendicular to each other
(2) The sum of any 3 angles in the quadrilateral is 270 degrees


(1) Insufficient. The diagonals of a rectangle could be perpendicular to each other (then it's a square) or not.
(2) The sum of 4 angles in the quadrilateral is 360. Hence, any of 4 angles in the quadrilater is 90 degree. So ABCD is a rectangle.

The answer is B.

Please re look... When diagonals are parallel...it's a Rhombus...not a Rectangle.

Answer shud be A. If the diagonals are perpendicular it's not a Rectangle.sufficient.

B is not sufficient, as the sum doesn't give any clarity about which figure it is.

Correct me if wrong.

Omkar Kamat
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Re: Is quadrilateral ABCD a rectangle? [#permalink] New post   11 Sep 2017, 08:25
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The sum of any 3 angles in the quadrilateral is 270 degrees.

It means the 4th angle will be 90 degree only. Try to understand it like this: If sum of angles a, b and c = 270 degree then angle d will be 90 degree. If sum of angles a, b and d = 270degree then angle c will be 90 degree and so on. So, it is a rectangle.
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Is quadrilateral ABCD a rectangle? [#permalink] New post   29 Nov 2016, 08:30
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Omkar.kamat wrote:
nguyendinhtuong wrote:
GMATPrepNow wrote:
Is quadrilateral ABCD a rectangle?

(1) The diagonals (AC and BD) are perpendicular to each other
(2) The sum of any 3 angles in the quadrilateral is 270 degrees


(1) Insufficient. The diagonals of a rectangle could be perpendicular to each other (then it's a square) or not.
(2) The sum of 4 angles in the quadrilateral is 360. Hence, any of 4 angles in the quadrilater is 90 degree. So ABCD is a rectangle.

The answer is B.

Please re look... When diagonals are parallel...it's a Rhombus...not a Rectangle.

Answer shud be A. If the diagonals are perpendicular it's not a Rectangle.sufficient.

B is not sufficient, as the sum doesn't give any clarity about which figure it is.

Correct me if wrong.


Sorry but the diagonals of a quadrilateral will never be parallel.

Rhombus is a quadrilateral that its diagonals are perpendicular, not parallel, at the midpoint of each.

Also, a Rhombus could be a square, so it is a rectangle, but a rectangle isn't necessarily a Rhombus

A Rectangle is a quadrilateral with 4 right angles
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Re: Is quadrilateral ABCD a rectangle? [#permalink] New post   Updated on: 11 Sep 2017, 08:39
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GMATPrepNow wrote:
vikrantsharma725@gmail.com wrote:
A is clear that quadrilateral can be rhombus as diagonals of rhombus are also prependicular.

but why answer is B. as it can be square also since it is given in B that sum of any 3 sides is 270 degree. and it can be rectangle also. but if we combine B and A then diagonals of rectangle are prependicular and sum of 3 sides is also 270 degree.

so please tell me why not answer is C


Great question! In fact, it illustrates why I created the question in the first place.

A square is a type of rectangle. So, if the quadrilateral is a square, then we can also conclude that the quadrilateral is a rectangle.

From the Official Guide:
A parallelogram with right angles is a rectangle, and a rectangle with all sides of equal length is a square.

For more on this, here's a video:


I have a query for statement 2. We are told that sum of any 3 angles is 270. So how can we assume that each will be 90? It can be any value. So ans should be E. What am I missing?

Originally posted by goalMBA1990 on 03 Sep 2017, 18:40.
Last edited by goalMBA1990 on 11 Sep 2017, 08:39, edited 1 time in total.
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Re: Is quadrilateral ABCD a rectangle? [#permalink] New post   29 Nov 2016, 08:32
nguyendinhtuong wrote:
Omkar.kamat wrote:
nguyendinhtuong wrote:
[quote="GMATPrepNow"]Is quadrilateral ABCD a rectangle?

(1) The diagonals (AC and BD) are perpendicular to each other
(2) The sum of any 3 angles in the quadrilateral is 270 degrees


(1) Insufficient. The diagonals of a rectangle could be perpendicular to each other (then it's a square) or not.
(2) The sum of 4 angles in the quadrilateral is 360. Hence, any of 4 angles in the quadrilater is 90 degree. So ABCD is a rectangle.

The answer is B.

Please re look... When diagonals are parallel...it's a Rhombus...not a Rectangle.

Answer shud be A. If the diagonals are perpendicular it's not a Rectangle.sufficient.

B is not sufficient, as the sum doesn't give any clarity about which figure it is.

Correct me if wrong.


Sorry but the diagonals of a quadrilateral will never be parallel.

Rhombus is a quadrilateral that its diagonals are perpendicular, not parallel, at the midpoint of each.

Also, a Rhombus could be a square, so it is a rectangle, but a rectangle isn't necessarily a Rhombus[/quote]
Sorry. I meant perpendicular.

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Re: Is quadrilateral ABCD a rectangle? [#permalink] New post   29 Nov 2016, 10:13
A is clear that quadrilateral can be rhombus as diagonals of rhombus are also prependicular.

but why answer is B. as it can be square also since it is given in B that sum of any 3 sides is 270 degree. and it can be rectangle also. but if we combine B and A then diagonals of rectangle are prependicular and sum of 3 sides is also 270 degree.

so please tell me why not answer is C
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Re: Is quadrilateral ABCD a rectangle? [#permalink] New post   20 Dec 2016, 05:34
Perfect nguyendinhtuong :D
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Re: Is quadrilateral ABCD a rectangle? [#permalink] New post   11 Dec 2017, 10:26
is-quadrilateral-rstv-a-rectangle-130928 .Please check it.

Sum of angles T, S, R is 270 degree and angle V is 90 degree. Yet TSRV is not a rectangle. So correct me why the answer should not be E.
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Re: Is quadrilateral ABCD a rectangle? [#permalink] New post   20 Jun 2019, 07:42
B is correct

(1) is insufficient due to #7.

Let me make clearer in (1). If diagonals of ABCD are prependicular, ABCD could be a rhombus or not.
If ABCD is a rhombus, it could be a square or not.
If ABCD is a square, it's also a rectangle.

So (1) => ABCD could be a rectangle or not. Insufficient.

(2) A quadrilateral with 4 right angles is a rectangle. If ABCD is a square, it's clearly a rectangle since square is a special type of rectangle. In all cases, we have ABCD is a rectangle. So (2) is sufficient to answer the question.
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Re: Is quadrilateral ABCD a rectangle? [#permalink] New post   04 Jul 2023, 11:10
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