Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59674

In the figure shown above, line segment QR has length 12, an
[#permalink]
Show Tags
06 Mar 2014, 03:07
Question Stats:
74% (03:09) correct 26% (03:08) wrong based on 889 sessions
HideShow timer Statistics
The Official Guide For GMAT® Quantitative Review, 2ND EditionIn 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 Problem Solving Question: 135 Category: Geometry; Algebra Area; Seconddegree equations Page: 79 Difficulty: 600 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Math Expert
Joined: 02 Sep 2009
Posts: 59674

Re: In the figure shown above, line segment QR has length 12, an
[#permalink]
Show Tags
06 Mar 2014, 03:08
SOLUTIONIn 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. Answer: B.
_________________




Intern
Joined: 08 Jan 2014
Posts: 4

Re: In the figure shown above, line segment QR has length 12, an
[#permalink]
Show Tags
06 Mar 2014, 09:50
Ans B Since the area of the total Fig is given as 540. We can plug ans choices as follows A) 540144=396( not a perfect square, should be a perfect square because fig MPQT is given as a square) B)540216=324 (perfect square, thus sides are 18)C)540324= not a perfect square D)540360= not a perfect square E)540396=144 ( perfect square, but if both are 12 then the total area will come out to be 144*2 and not 540) Just another simpler approach . Let me know if i missed something




Director
Joined: 25 Apr 2012
Posts: 651
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: In the figure shown above, line segment QR has length 12, an
[#permalink]
Show Tags
06 Mar 2014, 03:51
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 Let the side of square MPQT be "X" Then area of rectangular region MRPS will be (12+X)*X= 540 Solving for Quadratic Eqn, we get X^2+12X540=0 or X= {12 +/ \sqrt{\((12)^24*540*1\)} }/ 2 or X = (12 +/ 48)/2 or X=18 or 30 because X cannot be negative So Area of rectangular region TQRS= 18*12 = 216 Ans is B Difficulty level 600 is okay.
_________________
“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.”



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1727
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: In the figure shown above, line segment QR has length 12, an
[#permalink]
Show Tags
06 Mar 2014, 19:47
Refer fig below: \(x^2 + 12x = 540\) \(x^2 + 12x  540 = 0\) x = 18 (Ignore ve value) Area TQRS = 18 x 12 = 216 = Answer = B
Attachments
Picture%201.png [ 7.07 KiB  Viewed 11900 times ]



Intern
Joined: 06 Jan 2014
Posts: 35

Re: In the figure shown above, line segment QR has length 12, an
[#permalink]
Show Tags
08 Mar 2014, 18:21
manusingh3 wrote: Ans B Since the area of the total Fig is given as 540. We can plug ans choices as follows A) 540144=396( not a perfect square, should be a perfect square because fig MPQT is given as a square) B)540216=324 (perfect square, thus sides are 18)C)540324= not a perfect square D)540360= not a perfect square E)540396=144 ( perfect square, but if both are 12 then the total area will come out to be 144*2 and not 540) Just another simpler approach . Let me know if i missed something How did you know 324 was a perfect square? you skipped that part



Manager
Joined: 20 Dec 2013
Posts: 222
Location: India

Re: In the figure shown above, line segment QR has length 12, an
[#permalink]
Show Tags
08 Mar 2014, 19:28
Option B. Let each side of square=x Given that, x(x+12)=540 Therefore x=18 We have to find, 12x=12*18=216
Posted from my mobile device



Intern
Joined: 03 Aug 2012
Posts: 19
Location: United States (OR)
Concentration: Finance, International Business
GPA: 3.53
WE: Analyst (Entertainment and Sports)

Re: In the figure shown above, line segment QR has length 12, an
[#permalink]
Show Tags
08 Mar 2014, 20:45
I'm confused on this one... I set up the equation correctly as 540 = x * (12 + x) (or 540 = x^2 + 12x) but how can I simplify from there? I don't know a good way on knowing that x = 18. Any help would be greatly appreciated. Thanks.



Director
Joined: 25 Apr 2012
Posts: 651
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: In the figure shown above, line segment QR has length 12, an
[#permalink]
Show Tags
08 Mar 2014, 22:12
dbiersdo wrote: I'm confused on this one... I set up the equation correctly as 540 = x * (12 + x) (or 540 = x^2 + 12x) but how can I simplify from there? I don't know a good way on knowing that x = 18. Any help would be greatly appreciated. Thanks. Hi, Well you can solve the equation in second degree by factorizing the same x^2+12x540=0 Solving equations of degree 2 : QUADRATICThe general form of a quadratic equation is \(ax^2+bx+c=0\) This equation has 2 solutions given by \(\frac{b \pm \sqrt{b^24ac}}{2a}\) if \(b^2>4ac\)The equation has no solution if \(b^2<4ac\) The equation has exactly one solution if \(b^2=4ac\) [/color] When you solve the equation using the above , we get 2 values of x which are 30 and 18...Now x can't be negative so you take the positive value which is 18.
You may also want to refer to GMAT Club Math Book where you can find information on GMAT Math. For Algebra, you may refer to the the link algebra101576.html#p787276Another way to solve the quadratic as in the above case to plug in the answer choices and see which one fits. Plugin probably will be the quickest method. I missed that one Hope it helps
_________________
“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.”



Intern
Joined: 08 Jan 2014
Posts: 4

Re: In the figure shown above, line segment QR has length 12, an
[#permalink]
Show Tags
09 Mar 2014, 01:11
TroyfontaineMacon wrote: manusingh3 wrote: Ans B Since the area of the total Fig is given as 540. We can plug ans choices as follows A) 540144=396( not a perfect square, should be a perfect square because fig MPQT is given as a square) B)540216=324 (perfect square, thus sides are 18)C)540324= not a perfect square D)540360= not a perfect square E)540396=144 ( perfect square, but if both are 12 then the total area will come out to be 144*2 and not 540) Just another simpler approach . Let me know if i missed something How did you know 324 was a perfect square? you skipped that part Its just something I memorized. All squares up to 25. Its easy and will help you on the exam day With equations and Right angle triangles(Pythagorean triples etc.



Intern
Status: Going the extra mile
Joined: 08 Feb 2014
Posts: 14
Location: Netherlands
Concentration: Strategy, International Business
GMAT 1: 470 Q37 V18 GMAT 2: 570 Q36 V32 GMAT 3: 560 Q37 V30 GMAT 4: 610 Q41 V34

Re: In the figure shown above, line segment QR has length 12, an
[#permalink]
Show Tags
23 Apr 2014, 03:05
Total area = 540 Totale area = Total Length * Total Width Possible Length * Width: 60*9 30*18 15*36 We know that the sides of PQMT are equal ( = square ) 6012=48 and 9 ( not equal ) 3012=18 and 18 ( EQUAL !) Total Area  Area Square = Area Rectangle = 540  (18*18) = 216 . ANSWER B
_________________
Structural persistence is the key to succes . Party hard, study harder.
Still bashing, will continue to do so , although it's important to chill aswell ; ) STUDY+CHILL=VICTORY



Intern
Joined: 23 May 2015
Posts: 17

Re: In the figure shown above, line segment QR has length 12, an
[#permalink]
Show Tags
20 Jun 2015, 11:29
Bunuel wrote: SOLUTIONIn 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. Answer: B. What is the best way to solve complex quadratics like this one? I couldn't figure out x^2 + 12x  540 = 0 quick enough. Thanks.



Math Expert
Joined: 02 Sep 2009
Posts: 59674

Re: In the figure shown above, line segment QR has length 12, an
[#permalink]
Show Tags
20 Jun 2015, 12:47
bluepulaski1 wrote: Bunuel wrote: SOLUTIONIn 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. Answer: B. What is the best way to solve complex quadratics like this one? I couldn't figure out x^2 + 12x  540 = 0 quick enough. Thanks. Factoring Quadratics: http://www.purplemath.com/modules/factquad.htmSolving Quadratic Equations: http://www.purplemath.com/modules/solvquad.htm
_________________



Manager
Joined: 07 Apr 2015
Posts: 152

Re: In the figure shown above, line segment QR has length 12, an
[#permalink]
Show Tags
22 Jun 2015, 05:43
WoundedTiger wrote: dbiersdo wrote: I'm confused on this one... I set up the equation correctly as 540 = x * (12 + x) (or 540 = x^2 + 12x) but how can I simplify from there? I don't know a good way on knowing that x = 18. Any help would be greatly appreciated. Thanks. Hi, Well you can solve the equation in second degree by factorizing the same x^2+12x540=0 Solving equations of degree 2 : QUADRATICThe general form of a quadratic equation is \(ax^2+bx+c=0\) This equation has 2 solutions given by \(\frac{b \pm \sqrt{b^24ac}}{2a}\) if \(b^2>4ac\)The equation has no solution if \(b^2<4ac\) The equation has exactly one solution if \(b^2=4ac\) [/color] When you solve the equation using the above , we get 2 values of x which are 30 and 18...Now x can't be negative so you take the positive value which is 18.
You may also want to refer to GMAT Club Math Book where you can find information on GMAT Math. For Algebra, you may refer to the the link algebra101576.html#p787276Another way to solve the quadratic as in the above case to plug in the answer choices and see which one fits. Plugin probably will be the quickest method. I missed that one Hope it helps How is that an answer to his question? When you use this approach you will have to know the square root of 576 which is no easier to solve for...



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: In the figure shown above, line segment QR has length 12, an
[#permalink]
Show Tags
22 Jun 2015, 05:55
noTh1ng wrote: Well you can solve the equation in second degree by factorizing the same
x^2+12x540=0
How is that an answer to his question? When you use this approach you will have to know the square root of 576 which is no easier to solve for... Hi noTh1ng, Best way to solve the quadratic as in the above case is to plug in the answer choices and see which one fits. Plugin probably will be the quickest method. Second possibility is to prime factorise the number 540 i.e. 540 = 54 x 10 = 2x3x3x 3x2x5 = now see if any combination of two parts of these numbers make sum or difference of the two as 12 (coefficient of x) 18 x 30 = 540 and 3018 = 12 so x^2+12x540=0 can be rewritten as x^2 + 30x  18x + 540 = 0 i.e. x(x+30) 18(x+30) = 0 i.e. (x+30)*(x18) = 0 i.e. x= 18 or 30 Dimensions are always positive numbers hence 30 can be rejected I hope this helps!
_________________
Prosper!!!GMATinsightBhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhihttp://www.GMATinsight.com/testimonials.htmlACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Senior Manager
Joined: 10 Mar 2013
Posts: 461
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

In the figure shown above, line segment QR has length 12, an
[#permalink]
Show Tags
06 Nov 2015, 12:41
dbiersdo wrote: I'm confused on this one... I set up the equation correctly as 540 = x * (12 + x) (or 540 = x^2 + 12x) but how can I simplify from there? I don't know a good way on knowing that x = 18. Any help would be greatly appreciated. Thanks. We can complete a square here: divide \((12/2)^2=36\) > and add 36 to both sides \(x^2+12x+36=540+36\) > \((x+6)^2=576\) x+6=+/24, x=18,30 Answer (B) we can use only +ve values It's by far not a 600 Level > I would say 650 (regarding 55%)



Manager
Joined: 05 Jul 2015
Posts: 93
Concentration: Real Estate, International Business
GPA: 3.3

Re: In the figure shown above, line segment QR has length 12, an
[#permalink]
Show Tags
22 Nov 2015, 12:44
I got frustrated trying to figure out X^2+12x540 so I picked random numbers and plugged in X.
20^2+12(20)=640 Pretty close!
15^2+12(15)=400something... Close too but opposite direction
So X is between 20 and 15.
Answer B



Intern
Joined: 10 Aug 2015
Posts: 18

Re: In the figure shown above, line segment QR has length 12, an
[#permalink]
Show Tags
13 Jun 2016, 10:54
DJ1986 wrote: I got frustrated trying to figure out X^2+12x540 so I picked random numbers and plugged in X.
20^2+12(20)=640 Pretty close!
15^2+12(15)=400something... Close too but opposite direction
So X is between 20 and 15.
Answer B Sorry to bump the topic! But it was the same thing for me when I faced X^2 + 12x  540. For me what works the best in cases like this is to do this: x(x + 12) = 540. Think about a number that multiplied by (itself + 12) will result in 540. Hope it helps.



Director
Joined: 20 Feb 2015
Posts: 737
Concentration: Strategy, General Management

Re: In the figure shown above, line segment QR has length 12, an
[#permalink]
Show Tags
17 Jun 2016, 02:26
PM*PR=540 pm*(PQ+12) =540 PQ(PQ+12) =540 ( MPQT is a square) PQ^2 +12PQ540 =0 PQ^2 +30PQ18PQ540=0 PQ=18=PM=QT area of TQRS = 12*18=216



Current Student
Joined: 01 Dec 2016
Posts: 102
Concentration: Finance, Entrepreneurship
WE: Investment Banking (Investment Banking)

Re: In the figure shown above, line segment QR has length 12, an
[#permalink]
Show Tags
04 Dec 2017, 12:22
Quick way to solve this is to work backward using answer choices: from question stem it is clear that the area of TQRS is 12*PQ try few smart values and you will find the way easily If PQ=10 then PQ^2 =100 and 12*PQ=120 the sum would be more than 220 therefore PQ must be more than 10 If PQ=20 then PQ^2 =400 and 12*PQ=240 the sum would be more than 540 therefore PQ is less than 20 A TQRS = 244 > PQ = 12 > total area = 388 <540 (so out) B TQRS = 216> PQ = 18 > total area = 540 C TQRS = 324> PQ = 26 > (out) D PQ >20 > out E PQ >20 > out Answer is B
_________________
What was previously considered impossible is now obvious reality. In the past, people used to open doors with their hands. Today, doors open "by magic" when people approach them




Re: In the figure shown above, line segment QR has length 12, an
[#permalink]
04 Dec 2017, 12:22



Go to page
1 2
Next
[ 25 posts ]



