Last visit was: 12 Jul 2024, 17:04 It is currently 12 Jul 2024, 17:04

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Verbal Expert
Joined: 18 Apr 2015
Posts: 29080
Own Kudos [?]: 34063 [2]
Given Kudos: 25479
Send PM
Verbal Expert
Joined: 18 Apr 2015
Posts: 29080
Own Kudos [?]: 34063 [0]
Given Kudos: 25479
Send PM
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 11864 [2]
Given Kudos: 136
Send PM
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]
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?
Verbal Expert
Joined: 18 Apr 2015
Posts: 29080
Own Kudos [?]: 34063 [0]
Given Kudos: 25479
Send PM
Re: In the figure shown above, line segment QR has length 12 and [#permalink]
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.
Verbal Expert
Joined: 18 Apr 2015
Posts: 29080
Own Kudos [?]: 34063 [0]
Given Kudos: 25479
Send PM
Re: In the figure shown above, line segment QR has length 12 and [#permalink]
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
Verbal Expert
Joined: 18 Apr 2015
Posts: 29080
Own Kudos [?]: 34063 [0]
Given Kudos: 25479
Send PM
Re: In the figure shown above, line segment QR has length 12 and [#permalink]
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
[#permalink]
Moderators:
GRE Instructor
46 posts
GRE Forum Moderator
17 posts
Moderator
1090 posts
GRE Instructor
218 posts

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