It is currently 16 Jul 2019, 06:03
My Tests

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.

Parallelogram PQRS has a perimeter of 24. PQ = 2QR and Angle

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
Joined: 20 May 2014
Posts: 282
Followers: 18

Kudos [?]: 50 [0], given: 220

CAT Tests
Parallelogram PQRS has a perimeter of 24. PQ = 2QR and Angle [#permalink] New post 29 Oct 2017, 04:02
00:00

Question Stats:

100% (02:23) correct 0% (00:00) wrong based on 4 sessions
Parallelogram PQRS has a perimeter of 24. PQ = 2QR and Angle PQR = 120 degrees. Parallelogram TQUV is formed by cutting out part of parallelogram PQRS so that angle TQU and PQR share the same angle. If TQUV is half the area of PRQS and TQ = 2QU, what is the perimeter of TQUV to nearest 0.1?

Enter your value

[Reveal] Spoiler: OA
17.0


Kudos for correct solution.
1 KUDOS received
Intern
Intern
Joined: 02 Mar 2019
Posts: 45
Followers: 0

Kudos [?]: 4 [1] , given: 48

CAT Tests
Re: Parallelogram PQRS has a perimeter of 24. PQ = 2QR and Angle [#permalink] New post 15 Apr 2019, 08:30
1
This post received
KUDOS
Hi Bunnel
Could you please post the solution for this?

Thanks so much!
2 KUDOS received
Intern
Intern
Joined: 16 Apr 2019
Posts: 1
Followers: 0

Kudos [?]: 2 [2] , given: 3

Re: Parallelogram PQRS has a perimeter of 24. PQ = 2QR and Angle [#permalink] New post 16 Apr 2019, 02:11
2
This post received
KUDOS
PQRS has perimeter of 24. Consider x to be a side, then other side can be 2x.
3x*2=24, x=4.
So sides are 4 and 8.
One angle is 120, means other angle is 60.
Take sine of 60, which gives perpendicular like this..
sine of 60=p/4
thus, p=root3*2
find area as, A=p*8, (base times perpendicular height)
Area of another parallelogram is half, so it should be p*4..................(1)
Similarly using trigonometry find perpendicular height of smaller parallelogram, it should be x root3/2. (Where x is a smaller side and 2x would be larger)
now this height should be multiplied with '2x' to get area of smaller parallelogram..
Compare this to (1)...
Get x, it should be equal to 2 root2, so the other side will be 4 root2..
Then perimeter would be 2 root2 + 4 root2 + 2 root2 + 4 root2..
that is, 12 root2.. = 12*1.41 = 16.9
For nearest 0,1...it should be 17.0

( I am new here, this is my first post, sorry if this is not the way the answered should be presented. )
Thank you.
1 KUDOS received
Founder
Founder
User avatar
Joined: 18 Apr 2015
Posts: 7322
Followers: 122

Kudos [?]: 1430 [1] , given: 6569

CAT Tests
Re: Parallelogram PQRS has a perimeter of 24. PQ = 2QR and Angle [#permalink] New post 16 Apr 2019, 03:06
1
This post received
KUDOS
Expert's post
Welcome on board. :)

It is fine the way you have formatted.

Could be a bit better but is not the problem. Here we are to learn.

As long as you follow the rules for posting we are always eager to help the students.


Here a list of useful link on our community. Keep in mind that the relevant posts are put at the top of the general page (quant and verbal) or at the top of the specific page you wanna visit (say The sub forum quantitative comparison question)

How to post a question on the board and the use of the tag (very important)

Quant - https://greprepclub.com/forum/how-to-po ... 12752.html
Verbal - https://greprepclub.com/forum/how-to-po ... 12927.html

The rules of the board https://greprepclub.com/forum/rules-for ... -1083.html

------------------------------------------------------------------------------------------------------------------------------------------------------

All the Official Guides in one directory (of course from then follow the links ) https://greprepclub.com/forum/the-offic ... -8020.html

All the PowerPrep (the free software Provided by ETS - who own the GRE) questions explained https://greprepclub.com/forum/gre-power ... -3118.html

All the powerprep question explained for free in pdf by Skypetutor https://greprepclub.com/forum/vince-and ... 12946.html

-----------------------------------------------------------------------------------------------------------------------------------------------------------

Our main quant directory with the most relevant GRE books

Quant - https://greprepclub.com/forum/the-last- ... -3523.html
Verbal - https://greprepclub.com/forum/the-last- ... -3488.html

All you need to know about the GRE https://greprepclub.com/forum/all-you-d ... -7924.html

Our guide for quantitative reasoning for the GRE exam https://greprepclub.com/forum/the-defin ... -8898.html

The study plan for the 2019 https://greprepclub.com/forum/gre-study ... -8885.html

-------------------------------------------------------------------------------------------------------------------------------------------------------------------------

And last but not least our test https://greprepclub.com/tests/

Hope this helps :)

Ask for further assistance.

PS: there are more resources here. Just take a look at the announcement/sticky posts or do a search via the search button https://greprepclub.com/forum/search.php

Regards

Ask for further assistance I have attached the GC quant book that after ten years of experience I do think is the only thing to have for the quant concepts.

Practice at least one hour per day but not more than two first in your areas of content weak then consolidate the strongest areas.
_________________

Get the 2 FREE GREPrepclub Tests

Intern
Intern
Joined: 02 Mar 2019
Posts: 45
Followers: 0

Kudos [?]: 4 [0], given: 48

CAT Tests
Re: Parallelogram PQRS has a perimeter of 24. PQ = 2QR and Angle [#permalink] New post 16 Apr 2019, 08:41
Thank you for the response viktorIartav, but what if we do not want to use trigonometry? Is there another way?
Founder
Founder
User avatar
Joined: 18 Apr 2015
Posts: 7322
Followers: 122

Kudos [?]: 1430 [0], given: 6569

CAT Tests
Re: Parallelogram PQRS has a perimeter of 24. PQ = 2QR and Angle [#permalink] New post 16 Apr 2019, 10:08
Expert's post
Trigonometry is not contemplated any more for the GRE exam.
_________________

Get the 2 FREE GREPrepclub Tests

1 KUDOS received
Founder
Founder
User avatar
Joined: 18 Apr 2015
Posts: 7322
Followers: 122

Kudos [?]: 1430 [1] , given: 6569

CAT Tests
Re: Parallelogram PQRS has a perimeter of 24. PQ = 2QR and Angle [#permalink] New post 16 Apr 2019, 10:10
1
This post received
KUDOS
Expert's post
let us take the first parallelogram. PQRS
PQ = 2QR
Perimeter - 2(PQ+QR)=2(2QR+QR)=6QR=24......QR=4 and PQ=2*4=8
Now let us see the area of PQRS
drop a perpendicular from Q on PS -> QA
Now PQA is 30-60-90 triangle as angle PQT = 120-90=30..
so if PQ is 8, height or PA will be \(8\sqrt{3}/2=4\sqrt{3}\)
Thus area = PS*QA = \(4*4\sqrt{3}\)=\(16\sqrt{3}\)...

so area of parallelogram TQUV is \(16\sqrt{3}/2=8\sqrt{3}\)..
now let QU be a, so TQ=2a...
height of TQUV will be TQ*\(\sqrt{3}/2=a\sqrt{3}\), as TQA' is also 30-60-90.
thus its area = \(a*a\sqrt{3}=a^2\sqrt{3}=8\sqrt{3}\), so \(a=2\sqrt{2}\)..
thus perimeter is 2(a+2a)=6a=6*\(2\sqrt{2}=12*1.414=17\)
_________________

Get the 2 FREE GREPrepclub Tests

Re: Parallelogram PQRS has a perimeter of 24. PQ = 2QR and Angle   [#permalink] 16 Apr 2019, 10:10
Display posts from previous: Sort by

Parallelogram PQRS has a perimeter of 24. PQ = 2QR and Angle

  Question banks Downloads My Bookmarks Reviews Important topics  


GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.