GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Nov 2019, 08:47 ### 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

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

Author Message
TAGS:

### Hide Tags

Manager  B
Joined: 18 Jul 2013
Posts: 73
Location: Italy
GMAT 1: 600 Q42 V31 GMAT 2: 700 Q48 V38 GPA: 3.75
In the figure shown above, line segment QR has length 12 and rectangle  [#permalink]

### Show Tags

8
43 00:00

Difficulty:   55% (hard)

Question Stats: 73% (02:58) correct 27% (03:00) wrong based on 834 sessions

### HideShow timer Statistics 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

Attachment: Picture 1.png [ 6.97 KiB | Viewed 27016 times ]

Originally posted by oss198 on 05 Jan 2014, 16:49.
Last edited by Bunuel on 30 Jan 2018, 21:03, edited 2 times in total.
Edited the question.
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9784
Location: Pune, India
Re: In the figure shown above, line segment QR has length 12 and rectangle  [#permalink]

### Show Tags

15
9
oss198 wrote:
Thank you for your answer, but still : how do you find 48 quickly? you don't find the root of 12^2-4*540 so easily, do you?

ps : your signature is awesome

It's easy to solve this equation without using the formula (which is cumbersome in my opinion)
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

Here is a post discussing how to split the middle term quickly: http://www.veritasprep.com/blog/2013/12 ... equations/
_________________
Karishma
Veritas Prep GMAT Instructor

Manager  Joined: 20 Dec 2013
Posts: 116
Re: In the figure shown above, line segment QR has length 12 and rectangle  [#permalink]

### Show Tags

13
8
oss198 wrote:
Attachment:
Picture 1.png
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

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

_________________
76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views

Perfect Scores
http://perfectscores.org
##### General Discussion
Math Expert V
Joined: 02 Sep 2009
Posts: 59074
Re: In the figure shown above, line segment QR has length 12 and rectangle  [#permalink]

### Show Tags

1
2 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

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.

_________________
Manager  B
Joined: 18 Jul 2013
Posts: 73
Location: Italy
GMAT 1: 600 Q42 V31 GMAT 2: 700 Q48 V38 GPA: 3.75
Re: In the figure shown above, line segment QR has length 12 and rectangle  [#permalink]

### Show Tags

Bunuel wrote:

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.

Hi Bunuel, thank you for the answer, can you explain your technique to find the x quickly? It takes me a lot of time..
Director  Joined: 25 Apr 2012
Posts: 654
Location: India
GPA: 3.21
Re: In the figure shown above, line segment QR has length 12 and rectangle  [#permalink]

### Show Tags

oss198 wrote:
Bunuel wrote:

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.

Hi Bunuel, thank you for the answer, can you explain your technique to find the x quickly? It takes me a lot of time..

If I may,

To find the roots of the equation ax^2+bx+c=0 by the formulae

This equation has 2 solutions given by (-b+/-$$\sqrt{b^2-4ac}$$)/2a------>

(-12+/-$$\sqrt{12^2-4*540}$$)/2
So Roots are (-12 +/-48 )/2------> -30 and 18 since length cannot be negative so X=18 and therefore the area =18*12----->216
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
Manager  B
Joined: 18 Jul 2013
Posts: 73
Location: Italy
GMAT 1: 600 Q42 V31 GMAT 2: 700 Q48 V38 GPA: 3.75
Re: In the figure shown above, line segment QR has length 12 and rectangle  [#permalink]

### Show Tags

1
WoundedTiger wrote:
oss198 wrote:
Bunuel wrote:

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.

Hi Bunuel, thank you for the answer, can you explain your technique to find the x quickly? It takes me a lot of time..

If I may,

To find the roots of the equation ax^2+bx+c=0 by the formulae

This equation has 2 solutions given by (-b+/-$$\sqrt{b^2-4ac}$$)/2a------>

(-12+/-$$\sqrt{12^2-4*540}$$)/2
So Roots are (-12 +/-48 )/2------> -30 and 18 since length cannot be negative so X=18 and therefore the area =18*12----->216

Thank you for your answer, but still : how do you find 48 quickly? you don't find the root of 12^2-4*540 so easily, do you?

ps : your signature is awesome
SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1729
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: In the figure shown above, line segment QR has length 12 and rectangle  [#permalink]

### Show Tags

2
Factorize 540 & pick up the best fit
540
= 2 x 270
= 2 x 2 x 135
= 2 x 2 x 3 x 45
= 2 x 2 x 3 x 3 x 3 x 5

Rearranging:
= (2 x 3 x 5) x (2 x 3 x 3)
No. in above brackets add upto as 30 & 18; there multiplication is 540 & substraction is 12, so they best fit in the equation
_________________
Kindly press "+1 Kudos" to appreciate Intern  Joined: 25 May 2014
Posts: 18
GPA: 3.55
Re: In the figure shown above, line segment QR has length 12 and rectangle  [#permalink]

### Show Tags

VeritasPrepKarishma wrote:
oss198 wrote:
Thank you for your answer, but still : how do you find 48 quickly? you don't find the root of 12^2-4*540 so easily, do you?

ps : your signature is awesome

It's easy to solve this equation without using the formula (which is cumbersome in my opinion)
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

Here is a post discussing how to split the middle term quickly: http://www.veritasprep.com/blog/2013/12 ... equations/

Hi Karishma, obviously another awesome post! The blog post helped me a lot.

Would you say though that this technique would be even faster than simply back-solving when it comes to quadratic equations?

Thanks

Franco
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9784
Location: Pune, India
Re: In the figure shown above, line segment QR has length 12 and rectangle  [#permalink]

### Show Tags

1
francoimps wrote:
Would you say though that this technique would be even faster than simply back-solving when it comes to quadratic equations?

Thanks

Franco

Backsolving is a useful technique but its relevance in GMAT is decreasing. The options given are such that it is harder to back solve now. For example, here you will need to divide the option by 12 (the length of QR) and then try to plug in what you get in the equation. Notice that all options are divisible by 12 (which will be true for all good options) so it might be some time before you arrive at the answer using backsolving. During the exam, use whatever comes to your mind - you wouldn't have the time to consciously decide to use one method over another.
_________________
Karishma
Veritas Prep GMAT Instructor

Manager  B
Joined: 26 Mar 2017
Posts: 105
Re: In the figure shown above, line segment QR has length 12 and rectangle  [#permalink]

### Show Tags

well I found the correct equation within seconds but then I could not find the roots fast enough

Is there any shortcut/trick to find the roots ?
_________________
I hate long and complicated explanations!
Math Expert V
Joined: 02 Sep 2009
Posts: 59074
Re: In the figure shown above, line segment QR has length 12 and rectangle  [#permalink]

### Show Tags

daviddaviddavid wrote:
well I found the correct equation within seconds but then I could not find the roots fast enough

Is there any shortcut/trick to find the roots ?

Theory on Algebra: http://gmatclub.com/forum/algebra-101576.html
Algebra - Tips and hints: http://gmatclub.com/forum/algebra-tips- ... 75003.html

DS Algebra Questions to practice: http://gmatclub.com/forum/search.php?se ... &tag_id=29
PS Algebra Questions to practice: http://gmatclub.com/forum/search.php?se ... &tag_id=50

Hope it helps.
_________________
Manager  B
Joined: 26 Mar 2017
Posts: 105
Re: In the figure shown above, line segment QR has length 12 and rectangle  [#permalink]

### Show Tags

Bunuel wrote:
daviddaviddavid wrote:
well I found the correct equation within seconds but then I could not find the roots fast enough

Is there any shortcut/trick to find the roots ?

Theory on Algebra: http://gmatclub.com/forum/algebra-101576.html
Algebra - Tips and hints: http://gmatclub.com/forum/algebra-tips- ... 75003.html

DS Algebra Questions to practice: http://gmatclub.com/forum/search.php?se ... &tag_id=29
PS Algebra Questions to practice: http://gmatclub.com/forum/search.php?se ... &tag_id=50

Hope it helps.

thx Bunuel

ill check it

I guess my problem is just the high number of 540 but unfortunately the GMAT often uses such high number in quadratic equations related to these kind of geometric problems _________________
I hate long and complicated explanations!
Manager  B
Joined: 23 Dec 2013
Posts: 138
Location: United States (CA)
GMAT 1: 710 Q45 V41 GMAT 2: 760 Q49 V44 GPA: 3.76
Re: In the figure shown above, line segment QR has length 12 and rectangle  [#permalink]

### Show Tags

1
oss198 wrote:
Attachment:
Picture 1.png
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

First re-draw the image on the page and replace QR with 12 and PQ with x. We know that PM is also x, so the total area is (12+x)*x = 540. It turns into the quadratic 12x + x^2 = 540 or -540 + x^2 + 12x. The toughest part of the problem is figuring out which factor roots to use. The best method is to realize 540 is 9*60 and double 9 while halving 60 to get 18*30. These are separated by 12, the distance we need for the middle term of the quadratic (12x).

If x = 18 then the area of TQRS is 18*12 = 216.
Manager  G
Joined: 22 Nov 2016
Posts: 202
Location: United States (CA)
Schools: Haas EWMBA '22
GMAT 1: 640 Q43 V35 GPA: 3.4
Re: In the figure shown above, line segment QR has length 12 and rectangle  [#permalink]

### Show Tags

I was scratching my head when I saw 540 but when I wrote it as 54*10 and then 9*6*5*2, a light bulb lit up.
18 and 30. Now looking at the LHS to get 12 we need a larger positive number. This means 18 is the only option that stays non negative when factored.
_________________
Kudosity killed the cat but your kudos can save it.
Intern  Joined: 29 Sep 2017
Posts: 6
Re: In the figure shown above, line segment QR has length 12 and rectangle  [#permalink]

### Show Tags

PerfectScores wrote:
oss198 wrote:
Attachment:
Picture 1.png
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

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

Manager  B
Joined: 21 Jun 2017
Posts: 82
Re: In the figure shown above, line segment QR has length 12 and rectangle  [#permalink]

### Show Tags

oss198 wrote:
Attachment:
Picture 1.png
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

(12 + x) = length = PR
x = length of PQ
MP = PQ because square
therefore, no need for second variable, just use x again
(12 + x) (x) = 540
x^2 + 12x - 540 = 0
(x - 18 ) (x + 30) = 0
x = 18, -30

x= 18
18 x 12 = 216
Senior SC Moderator V
Joined: 22 May 2016
Posts: 3657
Re: In the figure shown above, line segment QR has length 12 and rectangle  [#permalink]

### Show Tags

ayas7 wrote:
PerfectScores wrote:
oss198 wrote:
Attachment:
Picture 1.png
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

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

ayas7 , a comment and links that might help. For questions where the answer choices are listed in ascending order, and we want to backsolve, we start with C because it is the middle value. C gives a benchmark.

If C yields an answer that is too large? Toss out Answers D and E, which will be greater than C. Then we only have to pick between Answers A and B.

There are two really good explanations for starting with C, given by a GMATclub expert, HERE
and HERE

THIS POST
by Bunuel includes the link I gave above, and a lot more. Scroll down slightly to "2. Strategies and Tactics."

One more. The post immediately above, which I just found rather accidentally, is part of what looks to be a phenomenal collection, Ultimate GMAT Quantitative Megathread, by Bunuel, composed of GMAT Quant . . . everything. MEGATHREAD HERE

Hope that helps.
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Never doubt that a small group of thoughtful, committed citizens can change the world; indeed, it's the only thing that ever has -- Margaret Mead
Math Expert V
Joined: 02 Sep 2009
Posts: 59074
Re: In the figure shown above, line segment QR has length 12 and rectangle  [#permalink]

### Show Tags

genxer123 wrote:
There are two really good explanations for starting with C, given by a GMATclub expert, HERE
and HERE

THIS POST
by Bunuel includes the link I gave above, and a lot more. Scroll down slightly to "2. Strategies and Tactics."

One more. The post immediately above, which I just found rather accidentally, is part of what looks to be a phenomenal collection, Ultimate GMAT Quantitative Megathread, by Bunuel, composed of GMAT Quant . . . everything. MEGATHREAD HERE

Hope that helps.

Backsolving on GMAT Math
How to Plug in Numbers on GMAT Math Questions
Why Approximate?
GMAT Math Strategies — Estimation, Rounding and other Shortcuts
The Power of Estimation for GMAT Quant
The 4 Math Strategies Everyone Must Master, Part 1 (1. Test Cases and 2. Choose Smart Numbers.)
The 4 Math Strategies Everyone Must Master, part 2 (3. Work Backwards and 4. Estimate)
Intelligent Guessing on GMAT
How to Avoid Tedious Calculations on the Quantitative Section of the GMAT
GMAT Tip of the Week: No Calculator? No Problem.
The Importance of Sorting Answer Choices on the GMAT
Identifying the Correct Answer on GMAT Quant Questions
How to Manage Unmanageable Numbers on the GMAT
_________________
Intern  B
Joined: 24 Oct 2017
Posts: 10
Location: United States (NY)
GMAT 1: 690 Q44 V40 GMAT 2: 710 Q44 V43 GPA: 3.25
Re: In the figure shown above, line segment QR has length 12 and rectangle  [#permalink]

### Show Tags

Some good explanations here. I got 95% of the way there: set up the quadratic and took the prime factor of 540, but it never clicked that it was 30 and 18. I'm not sure how I would solve such an equation on the actual examination. Re: In the figure shown above, line segment QR has length 12 and rectangle   [#permalink] 30 Jan 2018, 15:51

Go to page    1   2    Next  [ 24 posts ]

Display posts from previous: Sort by

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