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Re: Is quadrilateral ABCD a rectangle? [#permalink]

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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.

Re: Is quadrilateral ABCD a rectangle? [#permalink]

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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 When The Going Gets Tough, The Tough Gets Going !!

(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
_________________

Re: Is quadrilateral ABCD a rectangle? [#permalink]

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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.

Omkar Kamat When The Going Gets Tough, The Tough Gets Going !!

Re: Is quadrilateral ABCD a rectangle? [#permalink]

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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 When The Going Gets Tough, The Tough Gets Going !!

Re: Is quadrilateral ABCD a rectangle? [#permalink]

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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.

Re: Is quadrilateral ABCD a rectangle? [#permalink]

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29 Nov 2016, 10:25

Top Contributor

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.

Re: Is quadrilateral ABCD a rectangle? [#permalink]

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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.

Re: Is quadrilateral ABCD a rectangle? [#permalink]

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03 Sep 2017, 18:40

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?

Last edited by goalMBA1990 on 11 Sep 2017, 08:39, edited 1 time in total.

Re: Is quadrilateral ABCD a rectangle? [#permalink]

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11 Sep 2017, 08:25

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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