NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 16:27 It is currently 24 Apr 2024, 16:27
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

In square PQRS above, QR = 1, RU = US, and PT = TS. What is the area

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618811 [0]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
In square PQRS above, QR = 1, RU = US, and PT = TS. What is the area [#permalink] New post   11 Oct 2017, 00:46
Expert Reply
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

81% (01:52) correct 19% (01:31) wrong based on 73 sessions
Hide Show timer Statistics

In square PQRS above, QR = 1, RU = US, and PT = TS. What is the area of the quadrilateral PRUT?

(A) 1/8
(B) 1/4
(C) 3/8
(D) 5/8
(E) 2/3


Show Spoiler
Attachment:
2017-10-11_1127.png
2017-10-11_1127.png [ 4.3 KiB | Viewed 11292 times ]
ShowHide Answer
Official Answer
C
User avatar
S
Alexey1989x
Manager
Manager
Joined: 05 Dec 2016
Posts: 194
Own Kudos [?]: 88 [0]
Given Kudos: 49
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Send PM
GMAT ToolKit User
Re: In square PQRS above, QR = 1, RU = US, and PT = TS. What is the area [#permalink] New post   11 Oct 2017, 01:10
Area of PQRS = 1 ==> Areas of PRS=1/2
We know that iaw similarity properties:
Area of PRS/Area of TUS = RS^2/US^2= 1^2/0,5^2=1/0,25
Area of TUS = 1/8, therefore Area of PRTU = Area of PRS - Area of TUS = 1/2-1/8=3/8

Answer C.
User avatar
L
souvonik2k
Retired Moderator
Joined: 25 Nov 2015
Status:Preparing for GMAT
Posts: 972
Own Kudos [?]: 1988 [0]
Given Kudos: 751
Location: India
GPA: 3.64
Send PM
GMAT ToolKit User Reviews Badge
Re: In square PQRS above, QR = 1, RU = US, and PT = TS. What is the area [#permalink] New post   11 Oct 2017, 01:14
Side QR=1
Area of square PQRS = 1^2 =1
Area of triangle PRS = 1/2 of PQRS = 1/2
Area of triangle UTS = 1/2 * ST * SU = 1/2 *1/2 * 1/2 = 1/8
Area of quadrilateral PRUT = Area of triangle PRS - Area of triangle UTS =1/2 - 1/8 = 3/8
Answer C.
User avatar
P
JeffTargetTestPrep
Target Test Prep Representative
Joined: 04 Mar 2011
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Posts: 3043
Own Kudos [?]: 6272 [0]
Given Kudos: 1646
Send PM
Re: In square PQRS above, QR = 1, RU = US, and PT = TS. What is the area [#permalink] New post   13 Oct 2017, 09:29
Expert Reply
Bunuel wrote:

In square PQRS above, QR = 1, RU = US, and PT = TS. What is the area of the quadrilateral PRUT?

(A) 1/8
(B) 1/4
(C) 3/8
(D) 5/8
(E) 2/3


Show Spoiler
Attachment:
2017-10-11_1127.png


The area of square QRPS is 1 x 1 = 1.

The area of triangle QRP is 1/2.

The area of triangle TUS is 1/2 x 1/2 x 1/2 = 1/8.

Thus, the area of the quadrilateral PRUT is 1 - (1/2 + 1/8) = 1 - (4/8 + 1/8) = 3/8.

Answer: C
avatar
B
kaleem765
Intern
Intern
Joined: 24 Oct 2016
Posts: 23
Own Kudos [?]: 6 [0]
Given Kudos: 16
Send PM
GMAT ToolKit User
Re: In square PQRS above, QR = 1, RU = US, and PT = TS. What is the area [#permalink] New post   15 Oct 2017, 05:42
Area of PRUT = Area of PQRS - Area of UST - Area of PQR

Area of PQRS = 1*1 = 1

Since QR = PQ = 1 so Area of PQR = 1/2 * 1 * 1 = 1/2

Since RU = US = ST = PT = 1/2 so Area of UST = 1/2 * 1/2 * 1/2 = 1/8

So the area of PRUT = 1 -1/2 -1/8 = 3/8

ANSWER: C
User avatar
B
atulindia
Intern
Intern
Joined: 08 Mar 2017
Posts: 47
Own Kudos [?]: 24 [0]
Given Kudos: 28
Location: India
Concentration: Operations, General Management
GPA: 2.79
WE:Project Management (Manufacturing)
Send PM
Reviews Badge
Re: In square PQRS above, QR = 1, RU = US, and PT = TS. What is the area [#permalink] New post   15 Oct 2017, 06:40
Bunuel wrote:

In square PQRS above, QR = 1, RU = US, and PT = TS. What is the area of the quadrilateral PRUT?

(A) 1/8
(B) 1/4
(C) 3/8
(D) 5/8
(E) 2/3


Show Spoiler
Attachment:
2017-10-11_1127.png


If we divide square into triangles it would be 8 triangles of equal area
in shaded portion there are 3 triangles so ea of Quad is 3/8
Answer is C
User avatar
L
generis
Senior SC Moderator
Joined: 22 May 2016
Posts: 5330
Own Kudos [?]: 35486 [0]
Given Kudos: 9464
Send PM
CAT Tests
In square PQRS above, QR = 1, RU = US, and PT = TS. What is the area [#permalink] New post   15 Oct 2017, 08:50
Expert Reply
Bunuel wrote:

In square PQRS above, QR = 1, RU = US, and PT = TS. What is the area of the quadrilateral PRUT?

(A) 1/8
(B) 1/4
(C) 3/8
(D) 5/8
(E) 2/3

Show Spoiler
Attachment:
2017-10-11_1127.png

\((Area_{square}) - (Area_{2triangles}) = (Area_{quad})\)

Square side length = 1
Top triangle legs' length = 1
Bottom triangle legs' length* = \(\frac{1}{2}\)

Area of square: \(s^2 = 1^2 = 1\)
Area of top triangle: \(\frac{s^2}{2}=\frac{1}{2}\)
Area of bottom triangle: \(\frac{s^2}{2} \\
=\frac{(\frac{1}{4})}{2} = \frac{1}{8}\)

Both triangles' area:
\(\frac{1}{2} + \frac{1}{8} = \frac{5}{8}\)

Quadrilateral area: \(1 - \frac{5}{8}=\frac{3}{8}\)

Answer C

*The segments that constitute the legs of this right triangle are both \(\frac{1}{2}\) the length of the side of the square because they are half of a bisected side.
Square side RS is bisected; we are given that RU = US. Square side PS is similarly bisected.
GMAT Club Bot
gmatclubot
In square PQRS above, QR = 1, RU = US, and PT = TS. What is the area [#permalink]
15 Oct 2017, 08:50
Moderators:
Bunuel
Math Expert
92900 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