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555-605 (Medium)|   Geometry|      
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ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°. 23 May 2020, 08:53
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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25% (medium)

Question Stats:

65% (00:50) correct 35% (00:59) wrong based on 510 sessions

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ls quadrilateral RSTV a rectangle?

(1) The measure ∠RST of is 90°.
(2) The measure ∠TVR of is 90°.


DS20463
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E
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ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°. 22 Jun 2020, 05:54
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altairahmad
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.
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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
Screenshot 2020-06-22 at 18.24.02.png [ 16.66 KiB | Viewed 10817 times ]
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ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°. 23 May 2020, 09:15
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Bunuel
ls quadrilateral RSTV a rectangle?

(1) The measure ∠RST of is 90°.
(2) The measure ∠TVR of is 90°.


DS20463
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Properties of Rectangle:
- 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
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ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°. 24 May 2020, 10:46
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Bunuel
ls quadrilateral RSTV a rectangle?

(1) The measure ∠RST of is 90°.
(2) The measure ∠TVR of is 90°.


DS20463
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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.
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ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°. 25 May 2020, 12:55
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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
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ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°. 01 Jun 2020, 08:18
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Bunuel
ls quadrilateral RSTV a rectangle?

(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.
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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.
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ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°. 03 Jun 2020, 09:01
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NitishJain
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
Show more


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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ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°. 22 Jun 2020, 03:19
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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.
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ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°. 22 Jun 2020, 04:22
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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.


altairahmad
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.
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ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°. 22 Jun 2020, 04:50
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GMATBusters
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.


altairahmad
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.
Show more

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.
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ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°. 22 Jun 2020, 05:11
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Yes it is possible.
Please see the figure, you will understand.
Attachment:
WhatsApp Image 2020-06-22 at 5.40.45 PM.jpeg
WhatsApp Image 2020-06-22 at 5.40.45 PM.jpeg [ 11.94 KiB | Viewed 9929 times ]


altairahmad
GMATBusters
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.


altairahmad
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.

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.
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ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°. 26 Oct 2023, 20:59
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