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ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°.
[#permalink]
23 May 2020, 07:53
23 May 2020, 07:53
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ls quadrilateral RSTV a rectangle?
(1) The measure ∠RST of is 90°.
(2) The measure ∠TVR of is 90°.
DS20463
_________________
(1) The measure ∠RST of is 90°.
(2) The measure ∠TVR of is 90°.
DS20463
_________________
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Re: ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°.
[#permalink]
22 Jun 2020, 04:54
22 Jun 2020, 04:54
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altairahmad wrote:
Bunuel chetan2u VeritasKarishma GMATBusters
Are we going for E because we are taking 'rectangle' as literally a rectangle i.e 2 pairs of opposite sides equal and parallel ? What other shape can be with two opposite angles 90 each ? If its a square then it is a subset of rectangle, otherwise it is a rectangle.
Confused here.
Are we going for E because we are taking 'rectangle' as literally a rectangle i.e 2 pairs of opposite sides equal and parallel ? What other shape can be with two opposite angles 90 each ? If its a square then it is a subset of rectangle, otherwise it is a rectangle.
Confused here.
Think about it: Take a rectangle and split it into two 90 degree angles (each with two unequal sides).
Now you can join them back to make a rectangle but what if you flip them and join? (longer side with longer side) Do you still get a rectangle?
Attachment:
Screenshot 2020-06-22 at 18.24.02.png [ 16.66 KiB | Viewed 9098 times ]
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General Discussion
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ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°.
[#permalink]
23 May 2020, 08:15
23 May 2020, 08:15
1
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Expert Reply
Bunuel wrote:
ls quadrilateral RSTV a rectangle?
(1) The measure ∠RST of is 90°.
(2) The measure ∠TVR of is 90°.
DS20463
(1) The measure ∠RST of is 90°.
(2) The measure ∠TVR of is 90°.
DS20463
Properties of Rectangle:
- It's a parallelogram
- All angles are 90º
- Diagonals are equal
- It's a parallelogram
- All angles are 90º
- Diagonals are equal
Question: Is RSTV a rectangle?
Statement 1: ∠RST = 90°.
NOT SUFFICIENT
Statement 2: ∠TVR = 90°.
NOT SUFFICIENT
Combining the two statements
After combining the two statements we can observe that two diagonally oppositve vertices of a quadrilateral are forming 90º each
But the length of the sides have no relationship to ensure that it's a parallelogram and hence a rectangel
Hence
NOT SUFFICIENT
ANswer: Option E
Retired Moderator
Joined: 05 May 2016
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Re: ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°.
[#permalink]
24 May 2020, 09:46
24 May 2020, 09:46
Bunuel wrote:
ls quadrilateral RSTV a rectangle?
(1) The measure ∠RST of is 90°.
(2) The measure ∠TVR of is 90°.
DS20463
(1) The measure ∠RST of is 90°.
(2) The measure ∠TVR of is 90°.
DS20463
Statement 1: The measure ∠RST of is 90°.
=> 1 internal angle is 90°.
Clearly Insufficient.
Statement 2: The measure ∠TVR of is 90°.
=> 1 internal angle is 90°.
Clearly Insufficient.
Statement 1 + Statement 2: ∠RST and ∠TVR = 90°
=> could be a square or a rectangle.
Again Insufficient.
Answer E.
Re: ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°.
[#permalink]
25 May 2020, 11:55
25 May 2020, 11:55
quadrilateral RSTV a rectangle.
For a rectangle, all angles need to be 90 degrees and opposite sides equal.
Statement 1: ∠RST is 90°
NOT SUFFICIENT
Statement 2: ∠TVR is 90°
NOT SUFFICIENT
Let's combine statement 1 & 2::
opposite angles are 90 degrees each hence all four angles are 90 degrees respectively.
But it can be square or rectangle.
NOT SUFFICIENT
Hence E
_________________
Cheers,
NJ
For a rectangle, all angles need to be 90 degrees and opposite sides equal.
Statement 1: ∠RST is 90°
NOT SUFFICIENT
Statement 2: ∠TVR is 90°
NOT SUFFICIENT
Let's combine statement 1 & 2::
opposite angles are 90 degrees each hence all four angles are 90 degrees respectively.
But it can be square or rectangle.
NOT SUFFICIENT
Hence E
_________________
Cheers,
NJ
Re: ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°.
[#permalink]
01 Jun 2020, 07:18
01 Jun 2020, 07:18
1
Kudos
bm2201 wrote:
Bunuel wrote:
ls quadrilateral RSTV a rectangle?
(1) The measure ∠RST of is 90°.
(2) The measure ∠TVR of is 90°.
DS20463
(1) The measure ∠RST of is 90°.
(2) The measure ∠TVR of is 90°.
DS20463
Statement 1: The measure ∠RST of is 90°.
=> 1 internal angle is 90°.
Clearly Insufficient.
Statement 2: The measure ∠TVR of is 90°.
=> 1 internal angle is 90°.
Clearly Insufficient.
Statement 1 + Statement 2: ∠RST and ∠TVR = 90°
=> could be a square or a rectangle.
Again Insufficient.
Answer E.
Square is a kind of rectangle, which has equal sides. So your analysis is wrong
The reason why E is the answer is that we can draw figures with angles different from 90º.
Re: ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°.
[#permalink]
03 Jun 2020, 08:01
03 Jun 2020, 08:01
1
Kudos
NitishJain wrote:
quadrilateral RSTV a rectangle.
For a rectangle, all angles need to be 90 degrees and opposite sides equal.
Statement 1: ∠RST is 90°
NOT SUFFICIENT
Statement 2: ∠TVR is 90°
NOT SUFFICIENT
Let's combine statement 1 & 2::
opposite angles are 90 degrees each hence all four angles are 90 degrees respectively.
But it can be square or rectangle.
NOT SUFFICIENT
Hence E
For a rectangle, all angles need to be 90 degrees and opposite sides equal.
Statement 1: ∠RST is 90°
NOT SUFFICIENT
Statement 2: ∠TVR is 90°
NOT SUFFICIENT
Let's combine statement 1 & 2::
opposite angles are 90 degrees each hence all four angles are 90 degrees respectively.
But it can be square or rectangle.
NOT SUFFICIENT
Hence E
But just because it could be a square or rectangle doesnt mean its insufficient. Aren't all squares also considered rectangles?
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Joined: 27 Mar 2017
Posts: 283
Location: Saudi Arabia
GMAT 1: 700 Q47 V39
GPA: 3.36
Re: ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°.
[#permalink]
22 Jun 2020, 02:19
22 Jun 2020, 02:19
Bunuel chetan2u VeritasKarishma GMATBusters
Are we going for E because we are taking 'rectangle' as literally a rectangle i.e 2 pairs of opposite sides equal and parallel ? What other shape can be with two opposite angles 90 each ? If its a square then it is a subset of rectangle, otherwise it is a rectangle.
Confused here.
Are we going for E because we are taking 'rectangle' as literally a rectangle i.e 2 pairs of opposite sides equal and parallel ? What other shape can be with two opposite angles 90 each ? If its a square then it is a subset of rectangle, otherwise it is a rectangle.
Confused here.
Re: ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°.
[#permalink]
22 Jun 2020, 03:22
22 Jun 2020, 03:22
1
Kudos
Expert Reply
Hi
The Quadrilateral with only one pair of opposite angles = 90 deg can be any random quadrilateral.
The other 2 angles can be (90, 90) or (30, 150), or (10, 170).
As long as the sum of other 2 angles = 180, we can have infinitely many possibilities.
_________________
The Quadrilateral with only one pair of opposite angles = 90 deg can be any random quadrilateral.
The other 2 angles can be (90, 90) or (30, 150), or (10, 170).
As long as the sum of other 2 angles = 180, we can have infinitely many possibilities.
altairahmad wrote:
Bunuel chetan2u VeritasKarishma GMATBusters
Are we going for E because we are taking 'rectangle' as literally a rectangle i.e 2 pairs of opposite sides equal and parallel ? What other shape can be with two opposite angles 90 each ? If its a square then it is a subset of rectangle, otherwise it is a rectangle.
Confused here.
Are we going for E because we are taking 'rectangle' as literally a rectangle i.e 2 pairs of opposite sides equal and parallel ? What other shape can be with two opposite angles 90 each ? If its a square then it is a subset of rectangle, otherwise it is a rectangle.
Confused here.
_________________
Senior Manager
Joined: 27 Mar 2017
Posts: 283
Location: Saudi Arabia
GMAT 1: 700 Q47 V39
GPA: 3.36
Re: ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°.
[#permalink]
22 Jun 2020, 03:50
22 Jun 2020, 03:50
GMATBusters wrote:
Hi
The Quadrilateral with only one pair of opposite angles = 90 deg can be any random quadrilateral.
The other 2 angles can be (90, 90) or (30, 150), or (10, 170).
As long as the sum of other 2 angles = 180, we can have infinitely many possibilities.
The Quadrilateral with only one pair of opposite angles = 90 deg can be any random quadrilateral.
The other 2 angles can be (90, 90) or (30, 150), or (10, 170).
As long as the sum of other 2 angles = 180, we can have infinitely many possibilities.
altairahmad wrote:
Bunuel chetan2u VeritasKarishma GMATBusters
Are we going for E because we are taking 'rectangle' as literally a rectangle i.e 2 pairs of opposite sides equal and parallel ? What other shape can be with two opposite angles 90 each ? If its a square then it is a subset of rectangle, otherwise it is a rectangle.
Confused here.
Are we going for E because we are taking 'rectangle' as literally a rectangle i.e 2 pairs of opposite sides equal and parallel ? What other shape can be with two opposite angles 90 each ? If its a square then it is a subset of rectangle, otherwise it is a rectangle.
Confused here.
Pardon my ignorance but if we change the other two angles from anything other than 90 deg each, will the originally fixed vertices of 90 deg stay at 90 ? I think that we will not be able to make a quadrilateral where 1 pair of opposite angles is 90 and other 2 are not.
ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°.
[#permalink]
22 Jun 2020, 04:11
22 Jun 2020, 04:11
1
Kudos
Expert Reply
Yes it is possible.
Please see the figure, you will understand.
WhatsApp Image 2020-06-22 at 5.40.45 PM.jpeg [ 11.94 KiB | Viewed 8350 times ]
Pardon my ignorance but if we change the other two angles from anything other than 90 deg each, will the originally fixed vertices of 90 deg stay at 90 ? I think that we will not be able to make a quadrilateral where 1 pair of opposite angles is 90 and other 2 are not.
_________________
Please see the figure, you will understand.
Attachment:
WhatsApp Image 2020-06-22 at 5.40.45 PM.jpeg [ 11.94 KiB | Viewed 8350 times ]
altairahmad wrote:
GMATBusters wrote:
Hi
The Quadrilateral with only one pair of opposite angles = 90 deg can be any random quadrilateral.
The other 2 angles can be (90, 90) or (30, 150), or (10, 170).
As long as the sum of other 2 angles = 180, we can have infinitely many possibilities.
The Quadrilateral with only one pair of opposite angles = 90 deg can be any random quadrilateral.
The other 2 angles can be (90, 90) or (30, 150), or (10, 170).
As long as the sum of other 2 angles = 180, we can have infinitely many possibilities.
altairahmad wrote:
Bunuel chetan2u VeritasKarishma GMATBusters
Are we going for E because we are taking 'rectangle' as literally a rectangle i.e 2 pairs of opposite sides equal and parallel ? What other shape can be with two opposite angles 90 each ? If its a square then it is a subset of rectangle, otherwise it is a rectangle.
Confused here.
Are we going for E because we are taking 'rectangle' as literally a rectangle i.e 2 pairs of opposite sides equal and parallel ? What other shape can be with two opposite angles 90 each ? If its a square then it is a subset of rectangle, otherwise it is a rectangle.
Confused here.
Pardon my ignorance but if we change the other two angles from anything other than 90 deg each, will the originally fixed vertices of 90 deg stay at 90 ? I think that we will not be able to make a quadrilateral where 1 pair of opposite angles is 90 and other 2 are not.
_________________
Re: ls quadrilateral RSTV a rectangle? (1) The measure RST of is 90°.
[#permalink]
26 Oct 2023, 19:59
26 Oct 2023, 19:59
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Re: ls quadrilateral RSTV a rectangle? (1) The measure RST of is 90°. [#permalink]
26 Oct 2023, 19:59
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