NEW HERE? LEARN MORE
closeclose
Last visit was: 02 May 2024, 08:24 It is currently 02 May 2024, 08:24
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Suppose that quadrilateral PQRS has four congruent sides and satisfies

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
P
twobagels
Manager
Manager
Joined: 12 Jul 2020
Posts: 137
Own Kudos [?]: 453 [3]
Given Kudos: 2893
Location: United States (CA)
WE:Science (Other)
Send PM
Suppose that quadrilateral PQRS has four congruent sides and satisfies [#permalink] New post   06 Apr 2021, 17:47
3
Bookmarks
00:00
A
B
C
D
E

Difficulty:

75% (hard)

Question Stats:

38% (02:05) correct 63% (01:55) wrong based on 40 sessions
Hide Show timer Statistics
Suppose that quadrilateral PQRS has four congruent sides and satisfies PQ = PR. What is the value of \(\frac{QS}{PR}\)?

A. \(\frac{1}{2}\)

B. 1

C. \(\frac{\sqrt{3}}{2}\)

D. \(\sqrt{2}\)

E. \(\sqrt{3}\)
ShowHide Answer
Official Answer
E
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11212
Own Kudos [?]: 32161 [1]
Given Kudos: 298
Send PM
Reviews Badge
Suppose that quadrilateral PQRS has four congruent sides and satisfies [#permalink] New post   08 Apr 2021, 04:41
1
Kudos
Expert Reply
twobagels wrote:
Suppose that quadrilateral PQRS has four congruent sides and satisfies PQ = PR. What is the value of \(\frac{QS}{PR}\)?

A. \(\frac{1}{2}\)

B. 1

C. \(\frac{\sqrt{3}}{2}\)

D. \(\sqrt{2}\)

E. \(\sqrt{3}\)



All sides are equal, making PQRS a rhombus. Now PR is a diagonal that is equal to the sides.

Thus PQR and PRS become equilateral triangle.
The diagonals PR and QS will bisect each other at 90.

\(\triangle PQO\) will make a 30-60-90 triangle with sides PO:OQ:PQ in ratio 1:\(\sqrt{3}\):2

So \(\frac{QO}{OP}=\frac{\sqrt{3}}{1}\)

\(\frac{2*QO}{2*OP}=\frac{\sqrt{3}}{1}\)

\(\frac{QS}{PR}=\sqrt{3}\)

E
Attachments

Untitled12.png
Untitled12.png [ 16.62 KiB | Viewed 1067 times ]

User avatar
B
danbrown9445
Intern
Intern
Joined: 01 Feb 2021
Posts: 47
Own Kudos [?]: 35 [0]
Given Kudos: 415
GMAT 1: 600 Q36 V38
GMAT 2: 710 Q49 V36
Send PM
Reviews Badge
Re: Suppose that quadrilateral PQRS has four congruent sides and satisfies [#permalink] New post   10 Jul 2022, 12:46
twobagels wrote:
Suppose that quadrilateral PQRS has four congruent sides and satisfies PQ = PR. What is the value of \(\frac{QS}{PR}\)?

A. \(\frac{1}{2}\)

B. 1

C. \(\frac{\sqrt{3}}{2}\)

D. \(\sqrt{2}\)

E. \(\sqrt{3}\)





Let PQ=QR=RS=PS=PR=1 ( Given)
O is the midpoint of segment QS.
QO is height of equilateral triangle PQR.
Then QO = \(\frac{\sqrt{3}}{2}\).
So QS = \(\sqrt{3}\) ( QS = 2*QO)
\(\frac{QS}{PR}\) = \(\frac{\sqrt{3}}{1}\)
User avatar
B
rdrdrd1201
Intern
Intern
Joined: 13 Nov 2019
Posts: 45
Own Kudos [?]: 11 [0]
Given Kudos: 15
Schools: HBS '26 (A) Wharton '26 (D) Booth '26 (A)
GMAT 1: 720 Q49 V38
Send PM
Reviews Badge
Re: Suppose that quadrilateral PQRS has four congruent sides and satisfies [#permalink] New post   10 Jul 2022, 16:41
hi -chetan2u , how do we know that this is not a square?
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11212
Own Kudos [?]: 32161 [0]
Given Kudos: 298
Send PM
Reviews Badge
Suppose that quadrilateral PQRS has four congruent sides and satisfies [#permalink] New post   10 Jul 2022, 18:34
Expert Reply
rdrdrd1201 wrote:
hi -chetan2u , how do we know that this is not a square?



The sides PQ and QR are equal. Also given is that PQ=PR. Thus PQR is an equilateral triangle, making angle PQR as 60.

This means PQR is not a square.
GMAT Club Bot
gmatclubot
Suppose that quadrilateral PQRS has four congruent sides and satisfies [#permalink]
10 Jul 2022, 18:34
Moderators:
Bunuel
Math Expert
93005 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions