Last visit was: 10 Nov 2025, 00:02 It is currently 10 Nov 2025, 00:02
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

Close

GRE Prep 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 GRE 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
PREVIOUS TOPIC
NEXT TOPIC

In the figure shown above, line segment QR has length 12 and

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 33861
Own Kudos [?]: 40360 [2]
Given Kudos: 26605
Send PM
In the figure shown above, line segment QR has length 12 and [#permalink] New post   22 Jul 2020, 02:19
Expert Reply
2
Bookmarks
00:00

Question Stats:

74% (02:26) correct 25% (02:47) wrong based on 47 sessions

Hide Show timer Statistics

Image
In the figure shown above, line segment QR has length 12, and rectangle MPQT is a square. If the area of rectangular region MPRS is 540, what is the area of rectangular region TQRS?

(A) 144
(B) 216
(C) 324
(D) 360
(E) 396
ShowHide Answer
Official Answer
B
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 33861
Own Kudos [?]: 40360 [0]
Given Kudos: 26605
Send PM
Re: In the figure shown above, line segment QR has length 12 and [#permalink] New post   22 Jul 2020, 02:20
Expert Reply
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!

For more GRE Quant Theory and Practice, see

GRE Prep Club - MATH Book for the GRE Exam
User avatar
P
GreenlightTestPrep
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12542 [2]
Given Kudos: 136
Send PM

Top Member of the Month
Re: In the figure shown above, line segment QR has length 12 and [#permalink] New post   22 Jul 2020, 07:10
1
1
Bookmarks
Carcass wrote:
Image
In the figure shown above, line segment QR has length 12, and rectangle MPQT is a square. If the area of rectangular region MPRS is 540, what is the area of rectangular region TQRS?

(A) 144
(B) 216
(C) 324
(D) 360
(E) 396
Show: ::
Attachment:
Picture 1.png


Add the given information...
Image


Let x = the length of each side of square MPQT
Image

GIVEN: The area of rectangular region MPRS is 540

In other words: (base)(height) = 540
Substitute values to get: (x + 12)(x) = 540
Expand: x² + 12x = 540
Set equal to zero: x² + 12x - 540 = 0
Factor: (x + 30)(x - 18) = 0
So, EITHER x = -30 OR x = 18

Since the length cannot be negative, it must be the case that x = 18

What is the area of rectangular region TQRS?
Area = (base)(height) = (12)(18) = 216

Answer: B

Cheers,
Brent
avatar
B
YashShar
Intern
Intern
Joined: 20 May 2024
Posts: 3
Own Kudos [?]: 0 [0]
Given Kudos: 14
Send PM
Re: In the figure shown above, line segment QR has length 12 and [#permalink] New post   24 May 2024, 10:59
how did you determine the height as 12, wouldn't the height be different from 12 as it is QR, and it is stated that only the MPQT is a square. So, we know that QR and TS can be 12, and with x that would make it 12+18, and that would be our base?
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 33861
Own Kudos [?]: 40360 [0]
Given Kudos: 26605
Send PM
Re: In the figure shown above, line segment QR has length 12 and [#permalink] New post   24 May 2024, 11:21
Expert Reply
The area of MPRS = the area of MPQT + the area of TQRS.

540 = x^2 + 12x --> x = 18.

The area of TQRS = 12*18 = 216.

Answer: B.
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 33861
Own Kudos [?]: 40360 [0]
Given Kudos: 26605
Send PM
Re: In the figure shown above, line segment QR has length 12 and [#permalink] New post   24 May 2024, 11:21
Expert Reply
x^2 + 12x - 540 = 0

We try to split 540 into two factors such that their difference is 12
540 = 54*10 = 18*3*10
You can see immediately that the 2 factors will be 18 and 30.

x^2 + 30x - 18x -540 = 0
(x + 30)(x - 18) = 0
x = 18
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 33861
Own Kudos [?]: 40360 [0]
Given Kudos: 26605
Send PM
Re: In the figure shown above, line segment QR has length 12 and [#permalink] New post   24 May 2024, 11:22
Expert Reply
Another approach

Area of rectangle.........Side QT.......Area of square.....Total area of the figure
(A) 144
(B) 216
(C) 324....................324/12=27.... 27*27 =729........... 729 + 324 = 1053
(D) 360
(E) 396

The total area was supposed to be 540 however it is 1053 hence we move up (go for smaller values). Now we know that answer is either A or B so we try any of them.


Area of rectangle.........Side QT.......Area of square.....Total area of the figure
(A) 144
(B) 216....................216/12 =18.....18*18 =324.......... 324 + 216 =540 (BINGO!)
(C) 324....................324/12=27.... 27*27 =729........... 729 + 324 = 1053
(D) 360
(E) 396

Answer is B.
Prep Club for GRE Bot
gmatclubot
Re: In the figure shown above, line segment QR has length 12 and [#permalink]
24 May 2024, 11:22
Moderators:
adewale223
GRE Instructor
132 posts
bronaugust
GRE Forum Moderator
37 posts
BrushMyQuant
Moderator
1141 posts
VibhuAnurag
GRE Instructor
234 posts
Nsp10
Moderator
39 posts
tyrant100
GRE Forum Moderator
125 posts

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

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact