GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 09 Dec 2018, 18:06

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Free GMAT Algebra Webinar

     December 09, 2018

     December 09, 2018

     07:00 AM PST

     09:00 AM PST

    Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
  • Free lesson on number properties

     December 10, 2018

     December 10, 2018

     10:00 PM PST

     11:00 PM PST

    Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

Is quadrilateral PQRS a parallelogram? (1) P, Q, R, S are the mid-poi

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

DS Forum Moderator
avatar
P
Joined: 21 Aug 2013
Posts: 1412
Location: India
Premium Member
Is quadrilateral PQRS a parallelogram? (1) P, Q, R, S are the mid-poi  [#permalink]

Show Tags

New post 25 Jun 2018, 10:06
1
6
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

14% (01:07) correct 86% (01:07) wrong based on 38 sessions

HideShow timer Statistics

Is quadrilateral PQRS a parallelogram?

(1) P, Q, R, S are the mid-points of sides AB, BC, CD and AD respectively of a trapezoid ABCD.

(2) Diagonals of quadrilateral PQRS bisect each other.
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7095
Re: Is quadrilateral PQRS a parallelogram? (1) P, Q, R, S are the mid-poi  [#permalink]

Show Tags

New post 28 Jun 2018, 06:12
2
amanvermagmat wrote:
Is quadrilateral PQRS a parallelogram?

(1) P, Q, R, S are the mid-points of sides AB, BC, CD and AD respectively of a trapezoid ABCD.

(2) Diagonals of quadrilateral PQRS bisect each other.



With 90% wrong, it shows lack of properties of a parallelogram....

(1) P, Q, R, S are the mid-points of sides AB, BC, CD and AD respectively of a trapezoid ABCD.
When midpoints are joined of the four sides of ANY quadrilateral, it forms a parallelogram
look at the sketch..
ABCD is a quadrilateral and PQRS forms another quadrilateral by joining the midpoints..
join diagonal DB....
in triangle ADB, PQ will be parallel and half of the diagonal DB as PQ is bisecting the other two sides..
similarly SR is also parallel and half of DB..
thus PQ||DB||SR and PQ=SR

similarly for the set of other opposite sides
hence the quadrilateral is parallelogram

sufficient

(2) Diagonals of quadrilateral PQRS bisect each other.
Again this is the property of a quadrilateral- if diagonals bisect each other, it is a parallelogram
ca be proven by similar triangles and congruency..
sufficient

D
Attachments

Untitled11.png
Untitled11.png [ 6.06 KiB | Viewed 534 times ]


_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

SVP
SVP
User avatar
D
Joined: 26 Mar 2013
Posts: 1904
Reviews Badge CAT Tests
Re: Is quadrilateral PQRS a parallelogram? (1) P, Q, R, S are the mid-poi  [#permalink]

Show Tags

New post 28 Jun 2018, 07:17
chetan2u wrote:
amanvermagmat wrote:
Is quadrilateral PQRS a parallelogram?

(1) P, Q, R, S are the mid-points of sides AB, BC, CD and AD respectively of a trapezoid ABCD.

(2) Diagonals of quadrilateral PQRS bisect each other.



With 90% wrong, it shows lack of properties of a parallelogram....

(1) P, Q, R, S are the mid-points of sides AB, BC, CD and AD respectively of a trapezoid ABCD.
When midpoints are joined of the four sides of ANY quadrilateral, it forms a parallelogram
look at the sketch..
ABCD is a quadrilateral and PQRS forms another quadrilateral by joining the midpoints..
join diagonal DB....
in triangle ADB, PQ will be parallel and half of the diagonal DB as PQ is bisecting the other two sides..
similarly SR is also parallel and half of DB..
thus PQ||DB||SR and PQ=SR

similarly for the set of other opposite sides
hence the quadrilateral is parallelogram

sufficient

(2) Diagonals of quadrilateral PQRS bisect each other.
Again this is the property of a quadrilateral- if diagonals bisect each other, it is a parallelogram
ca be proven by similar triangles and congruency..
sufficient

D


Hi chetan2u

In statement 2, Could the figure be square or rectangular? or are both subset/special case of parallelogram so they must be considered parallelogram?

Thanks
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7095
Re: Is quadrilateral PQRS a parallelogram? (1) P, Q, R, S are the mid-poi  [#permalink]

Show Tags

New post 28 Jun 2018, 07:51
Mo2men wrote:
chetan2u wrote:
amanvermagmat wrote:
Is quadrilateral PQRS a parallelogram?

(1) P, Q, R, S are the mid-points of sides AB, BC, CD and AD respectively of a trapezoid ABCD.

(2) Diagonals of quadrilateral PQRS bisect each other.



With 90% wrong, it shows lack of properties of a parallelogram....

(1) P, Q, R, S are the mid-points of sides AB, BC, CD and AD respectively of a trapezoid ABCD.
When midpoints are joined of the four sides of ANY quadrilateral, it forms a parallelogram
look at the sketch..
ABCD is a quadrilateral and PQRS forms another quadrilateral by joining the midpoints..
join diagonal DB....
in triangle ADB, PQ will be parallel and half of the diagonal DB as PQ is bisecting the other two sides..
similarly SR is also parallel and half of DB..
thus PQ||DB||SR and PQ=SR

similarly for the set of other opposite sides
hence the quadrilateral is parallelogram

sufficient

(2) Diagonals of quadrilateral PQRS bisect each other.
Again this is the property of a quadrilateral- if diagonals bisect each other, it is a parallelogram
ca be proven by similar triangles and congruency..
sufficient

D


Hi chetan2u

In statement 2, Could the figure be square or rectangular? or are both subset/special case of parallelogram so they must be considered parallelogram?

Thanks



Hi..

It can be rectangle or square..
Figure with four sides- quadrilateral
Parallelogram is a type of quadrilateral with opposite sides equal and parallel.
Rectangle is a type of parallelogram and each square is a rectangle..
Rhombus is a parallelogram and each square is also a rhombus
Apart from a parallelogram, trapezium is another type of quadrilateral
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

GMAT Club Bot
Re: Is quadrilateral PQRS a parallelogram? (1) P, Q, R, S are the mid-poi &nbs [#permalink] 28 Jun 2018, 07:51
Display posts from previous: Sort by

Is quadrilateral PQRS a parallelogram? (1) P, Q, R, S are the mid-poi

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.