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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°.

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Math Expert V
Joined: 02 Sep 2009
Posts: 65095
ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°.  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 55% (00:46) correct 45% (00:54) wrong based on 134 sessions

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

DS20463

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GMAT Club Legend  V
Status: GMATINSIGHT Tutor
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ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°.  [#permalink]

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Bunuel wrote:

(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

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

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RC Moderator G
Joined: 05 May 2016
Posts: 257
Location: India
Re: ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°.  [#permalink]

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Bunuel wrote:

(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.

IESE School Moderator S
Joined: 11 Feb 2019
Posts: 308
Re: ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°.  [#permalink]

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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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Joined: 21 Oct 2018
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Re: ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°.  [#permalink]

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bm2201 wrote:
Bunuel wrote:

(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.

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.
Intern  B
Joined: 23 Feb 2020
Posts: 6
Re: ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°.  [#permalink]

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1
NitishJain wrote:
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?
Manager  B
Joined: 27 Mar 2017
Posts: 172
Re: ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°.  [#permalink]

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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.
Retired Moderator V
Joined: 27 Oct 2017
Posts: 1843
WE: General Management (Education)
Re: ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°.  [#permalink]

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1
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.

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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Manager  B
Joined: 27 Mar 2017
Posts: 172
Re: ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°.  [#permalink]

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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.

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.
Retired Moderator V
Joined: 27 Oct 2017
Posts: 1843
WE: General Management (Education)
ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°.  [#permalink]

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1
Yes it is possible.
Please see the figure, you will understand.
Attachment: WhatsApp Image 2020-06-22 at 5.40.45 PM.jpeg [ 11.94 KiB | Viewed 321 times ]

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.

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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Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 10653
Location: Pune, India
Re: ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°.  [#permalink]

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3

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 308 times ]

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Karishma
Veritas Prep GMAT Instructor Re: ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°.   [#permalink] 22 Jun 2020, 04:54

# ls quadrilateral RSTV a rectangle? (1) The measure ∠RST of is 90°.  