Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 11 Jul 2010
Posts: 28

In the figure shown, what is the value of x? [#permalink]
Show Tags
25 Jul 2010, 20:24
9
This post received KUDOS
90
This post was BOOKMARKED
Question Stats:
66% (02:09) correct
34% (01:15) wrong based on 1515 sessions
HideShow timer Statistics
In the figure shown, what is the value of x? (1) The length of line segment QR is equal to the length of line segment RS (2) The length of line segment ST is equal to the length of line segment TU Attachment:
Triangle.GIF [ 2.17 KiB  Viewed 119615 times ]
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
"If everything seems under control, you're just not going fast enough."  Mario Andretti, ItalianAmerican racecar driver champion



Math Expert
Joined: 02 Sep 2009
Posts: 39673

Re: In the figure shown, what is the value of x? [#permalink]
Show Tags
26 Jul 2010, 14:56
64
This post received KUDOS
Expert's post
85
This post was BOOKMARKED
In the figure shown, what is the value of x?\(x+\angle{QSR}+\angle{UST}=180\) (straight line =180) and \(\angle{R}+\angle{T}=90\) (as PRT is right angle) (1) The length of line segment QR is equal to the length of line segment RS > triangle QRS is isosceles > \(\angle{RQS}=\angle{QSR}=\frac{180\angle{R}}{2}\) (as \(\angle{RQS}+\angle{QSR}+\angle{R}=180\) > \(2*\angle{QSR}+\angle{R}=180\) > \(\angle{QSR}=\frac{180\angle{R}}{2}\)). Not sufficient. (2) The length of line segment ST is equal to the length of line segment TU > triangle UST is isosceles > \(\angle{SUT}=\angle{UST}=\frac{180\angle{T}}{2}\). Not sufficient. (1)+(2) \(x+\angle{QSR}+\angle{UST}=180\) > \(x+\frac{180\angle{R}}{2}+\frac{180\angle{T}}{2}=180\) > \(x+\frac{360(\angle{R}+\angle{T})}{2}=180\) > since \(\angle{R}+\angle{T}=90\) > \(x+\frac{36090}{2}=180\) > \(x=45\). Sufficient. Answer: C.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 18 Aug 2009
Posts: 41
Location: United States
Concentration: Finance, Entrepreneurship
GPA: 3.29
WE: Engineering (Consulting)

Re: In the figure shown, what is the value of x? [#permalink]
Show Tags
05 Nov 2010, 18:32
3
This post received KUDOS
Well this is how I would solve this.
Original statement:
What is x?
Without jumping into statements, we can clearly see that x = 180  ARSQ  ATSU.
Statement 1:
Statement 1 says that triangle QRS is isosceles. with ARSQ = ARQS
therefore we know that ARSQ = (180  ASRQ)/2.
However, without information about triangle TSU cannot solve the above equation about x.
Insufficient
Statement 2:
Statement 2 says that triangle TSU is isosceles with ATSU = (180  ASTU)/2. Similar to statement 1, not enough information about triangle RSQ to find x.
Insufficient.
Statement 1 + 2:
From statement 1: we know that ARSQ = (180ASRQ)/2 From statement 2: we know that ATSU = (180ASTU)/2
Plugging these information into the x = 180  ARSQ  ATSU we see that
x = 180  (180ASRQ)/2  (180ASTU)/2 = 180  (360/2) + (ASRQ + ASTU)/2 = (ASRQ + ASTU)/2
Since we know points RTP makes a right triangle, we know that ASRQ + ASTU = 90.
x = 45.
Sufficient.
My answer would be C.



Manager
Joined: 05 Nov 2009
Posts: 63

Re: In the figure shown, what is the value of x? [#permalink]
Show Tags
05 Nov 2010, 19:10
My answer would be C as well, from the
Isosceles triangle give us 45 degree angle.
Statement 1 : we know that angle RSQ = 45 Statement 2 : We know that angle UST = 90 (SUT = 45, UTS = 45, UST = 180  (SUT + UTS)
Hence x equal with 180  (45 +95) = 45



Manager
Status: Fighting the beast.
Joined: 25 Oct 2010
Posts: 184
Schools: Pitt, Oregon, LBS...

Re: In the figure shown, what is the value of x? [#permalink]
Show Tags
20 Dec 2010, 14:57
Hey guys, I have another question regarding my reasoning in the solving of the problem. The official answer is: I originally answered and incorrectly so. Now that I looked at it more, I came up with this solution, and I'd appreciate if you can tell me if my logic is correct: Let's label angle QRS (or PRT) as w. Let's label angle STU as z. Since RPT is 90, we know that w+z=90 Now, RQS and RSQ are same angles. So, we can label them as j. At the same time, TSU and TUS are the same, so we can label them as k. We have that 2j+w=180, that 2k+z=180, and that w+z=90. By substituting, we can see that w=1802j and that z=1802k. Finally, we have that w+z=90 or that (1802j)+(1802k)=90 or that 2k+2j=250, or that j+k=125. Since j and k lie on a straight line, and combined with x produce 180, and j+k=125, we conclude that x=55. Is my reasoning alright and is there a quicker way to solve this? Much appreciated!
_________________
[highlight]Monster collection of Verbal questions (RC, CR, and SC)[/highlight] http://gmatclub.com/forum/massivecollectionofverbalquestionsscrcandcr106195.html#p832142
[highlight]Massive collection of thousands of Data Sufficiency and Problem Solving questions and answers:[/highlight] http://gmatclub.com/forum/1001dsquestionsfile106193.html#p832133



Math Expert
Joined: 02 Sep 2009
Posts: 39673

Re: In the figure shown, what is the value of x? [#permalink]
Show Tags
20 Dec 2010, 15:11
MisterEko wrote: Hey guys, I have another question regarding my reasoning in the solving of the problem. The official answer is: I originally answered and incorrectly so. Now that I looked at it more, I came up with this solution, and I'd appreciate if you can tell me if my logic is correct: Let's label angle QRS (or PRT) as w. Let's label angle STU as z. Since RPT is 90, we know that w+z=90 Now, RQS and RSQ are same angles. So, we can label them as j. At the same time, TSU and TUS are the same, so we can label them as k. We have that 2j+w=180, that 2k+z=180, and that w+z=90. By substituting, we can see that w=1802j and that z=1802k. Finally, we have that w+z=90 or that (1802j)+(1802k)=90 or that 2k+2j=250, or that j+k=125. Since j and k lie on a straight line, and combined with x produce 180, and j+k=125, we conclude that x=55. Is my reasoning alright and is there a quicker way to solve this? Much appreciated! Except the calculation (the red part) seems that everything is OK. Check other solutions above for slightly different approaches.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Status: Fighting the beast.
Joined: 25 Oct 2010
Posts: 184
Schools: Pitt, Oregon, LBS...

Re: In the figure shown, what is the value of x? [#permalink]
Show Tags
20 Dec 2010, 15:29
Thanks Bunnuel, I appreciate it. I see I made the wrong calculation, but the answer should be the same in this DS, which is C. If you have any suggestions as to how I can search problems that are posted in a form of an image rather than words, it would be helpful so I don't have to repeat Qs... Thanks again!
_________________
[highlight]Monster collection of Verbal questions (RC, CR, and SC)[/highlight] http://gmatclub.com/forum/massivecollectionofverbalquestionsscrcandcr106195.html#p832142
[highlight]Massive collection of thousands of Data Sufficiency and Problem Solving questions and answers:[/highlight] http://gmatclub.com/forum/1001dsquestionsfile106193.html#p832133



Math Expert
Joined: 02 Sep 2009
Posts: 39673

Re: In the figure shown, what is the value of x? [#permalink]
Show Tags
20 Dec 2010, 15:58
MisterEko wrote: Thanks Bunnuel, I appreciate it. I see I made the wrong calculation, but the answer should be the same in this DS, which is C.
If you have any suggestions as to how I can search problems that are posted in a form of an image rather than words, it would be helpful so I don't have to repeat Qs... Thanks again! Generally it's a good idea to search before posting. Though it's not a probelm to post a question that was posted before: if moderators find previous discussions they will merge the topics, copy the solution from there or give a link to it. To make it easier to search I always copy a body text of every question to the post. So for example I'd search this question in DS subforum by the key words: "figure", "shown", "segment", "length".
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Status: what we want to do, do it as soon as possible
Joined: 24 May 2010
Posts: 110
Location: Vietnam
WE 1: 5.0

Re: In the figure shown, what is the value of x? [#permalink]
Show Tags
16 Mar 2011, 01:03
Bunuel wrote: In the figure shown, what is the value of x?
x+<QSR+<UST=180 (straight line =180) and <R+<T=90 (as PRT is right angle)
(1) The length of line segment QR is equal to the length of line segment RS > QRS is isosceles > <PQS=<QSR=(180R)/2 (as <PQS+<QSR+<R=180 > 2<QSR+<R=180 > <QSR=(180R)/2). Not sufficient.
(2) The legnth of line segment ST is equal to the length of line segment TU > UST is isosceles > <SUT=<UST=(180T)/2. Not sufficient.
(1)+(2) x+<QSR+<UST=180 > x+(180R)/2+(180T)/2=180 > x+(360(R+T))/2=180 > as R+T=90 > x+(36090)/2=180 > x=45. Sufficient.
Answer: C. so kool
_________________
Consider giving me kudos if you find my explanations helpful so i can learn how to express ideas to people more understandable.



SVP
Joined: 16 Nov 2010
Posts: 1663
Location: United States (IN)
Concentration: Strategy, Technology

Re: In the figure shown, what is the value of x? [#permalink]
Show Tags
16 Mar 2011, 21:19
14
This post received KUDOS
3
This post was BOOKMARKED
From (1) RSQ = RQS From (2) SUT = TSU Because these 3 angles are on a straight line: x + RSQ + TSU = 180 As all the angles of a quadrilateral sum up to 360: x+90 + 180  RSQ + 180  TSU = 360 => x + 360  (RSQ + TSU) + 90 = 360 => x + 90 (180x) = 0 => 2x  90 = 0 => x = 45 So the answer is C.
_________________
Formula of Life > Achievement/Potential = k * Happiness (where k is a constant)
GMAT Club Premium Membership  big benefits and savings



Senior Manager
Joined: 30 Aug 2009
Posts: 287
Location: India
Concentration: General Management

Re: In the figure shown, what is the value of x? [#permalink]
Show Tags
08 Jan 2012, 06:17
kotela wrote: Can anyone please help me in solving this problem....... stmnt 1. QR= RS then angle RQS = angle RSQ = y We have no other detail and hence insuff stmnt 2: like stmnt 1 this will also be insuff taking together we have QR= RS then angle RQS = angle RSQ = y then angle QRS = 180  2y PTR = 180  ( 90 + 180  2y) = 2y  90 we have TSU = TUS = [180  (2y  90)]/2 = 135  y RSQ + QSU + TUS = 180 y + x + 135  y = 180 Hence C is Suff



Manager
Joined: 29 Jul 2011
Posts: 107
Location: United States

Re: In the figure shown, what is the value of x? [#permalink]
Show Tags
08 Jan 2012, 18:45
1
This post received KUDOS
C it is. Two equations, x = 180  (a + b), where a and b are RQS and SUT. x = 360 [(180a) + (180b) + 90] = (a+b)90. Solve both, you get x.
_________________
I am the master of my fate. I am the captain of my soul. Please consider giving +1 Kudos if deserved!
DS  If negative answer only, still sufficient. No need to find exact solution. PS  Always look at the answers first CR  Read the question stem first, hunt for conclusion SC  Meaning first, Grammar second RC  Mentally connect paragraphs as you proceed. Short = 2min, Long = 34 min



Senior Manager
Joined: 15 Jun 2010
Posts: 361
Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)

Re: In the figure shown, what is the value of x? [#permalink]
Show Tags
08 Aug 2012, 15:37
Hi Bunuel, I got the answer by plugging 2 diff values and I got the answer in a very short time. Am i doing anything wrong. Pls explain. My approach as follows: I did this by plugging 2 different sets of values. We know PRT is a right angle triangle. So let it be 906030 or 904545 triangle. Now we can find out the value of X for both this situation. In both case the value of X comes as 45 degree. So St 1+ St 2 Sufficient. For 906030: <RST + <TSU = 135 degree, so X =45 degree For 904545: <RST + <TSU = 135/2 + 135/2 = 135 Degree, so X =45 Degree
_________________
Regards SD  Press Kudos if you like my post. Debrief 610540580710(Long Journey): http://gmatclub.com/forum/from600540580710finallyachievedin4thattempt142456.html



Director
Joined: 14 Dec 2012
Posts: 832
Location: India
Concentration: General Management, Operations
GPA: 3.6

Re: In the figure shown, what is the value of x? [#permalink]
Show Tags
17 Jul 2013, 13:50
shorteverything wrote: Attachment: Triangle.GIF In the figure shown, what is the value of x? (1) The length of line segment QR is equal to the length of line segment RS (2) The length of line segment ST is equal to the length of line segment TU hi bunuel, just let me know if i go wrong. x = angle QSU===>This angle is dependent on two things: 1)QS orientation 2) SU orientation. statement 1 tell RS=RQ==>means orientation of QS is fixed===>but we dont know about SU==>INSUFFICIENT STATEMENT 2==> TU=TS==>orientation of SU fixed ==>but we dont know about QS.==>INSUFFICIENT. by combining both orientation of both QS and SU is fixed==>so will defenetely get fixed value. hence C
_________________
When you want to succeed as bad as you want to breathe ...then you will be successfull....
GIVE VALUE TO OFFICIAL QUESTIONS...
GMAT RCs VOCABULARY LIST: http://gmatclub.com/forum/vocabularylistforgmatreadingcomprehension155228.html learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmatanalyticalwritingassessment : http://www.youtube.com/watch?v=APt9ITygGss



Intern
Joined: 15 Jul 2012
Posts: 19
Location: India
Concentration: International Business, General Management
GMAT Date: 09272013
GPA: 3.04
WE: Information Technology (Computer Software)

Re: In the figure shown, what is the value of x? [#permalink]
Show Tags
31 Aug 2013, 13:57
Hi Subash, Could you please explain me how you got the eqn > x+90 + 180  RSQ + 180  TSU = 360 ? subhashghosh wrote: From (1) RSQ = RQS
From (2) SUT = TSU
Because these 3 angles are on a straight line:
x + RSQ + TSU = 180
As all the angles of a quadrilateral sum up to 360:
x+90 + 180  RSQ + 180  TSU = 360
=> x + 360  (RSQ + TSU) + 90 = 360
=> x + 90 (180x) = 0
=> 2x  90 = 0
=> x = 45
So the answer is C.



Senior Manager
Joined: 15 Aug 2013
Posts: 311

Re: In the figure shown, what is the value of x? [#permalink]
Show Tags
17 Jun 2014, 18:12
subhashghosh wrote: From (1) RSQ = RQS
From (2) SUT = TSU
Because these 3 angles are on a straight line:
x + RSQ + TSU = 180
As all the angles of a quadrilateral sum up to 360:
x+90 + 180  RSQ + 180  TSU = 360
=> x + 360  (RSQ + TSU) + 90 = 360
=> x + 90 (180x) = 0
=> 2x  90 = 0
=> x = 45
So the answer is C. Hi Subhash, I got a little lost in the middle of this solution. Can you please explain how you're equating the angles to 360. I realize that you're equating the quadrilateral PQSU but i'm not sure where you're getting all the angles from? Highlighted the above area in question. Isnt "180  RSQ + 180  TSU" actually giving you the the line "RT" if you add "x" in the mix of it? Another question  are we able to say that angle x is the sum of RQS and SRQ since they are opposite ends of the angle in question? Thanks!



Current Student
Status: Stay focused...
Joined: 20 Apr 2014
Posts: 445
Location: United States (MI)
Concentration: Finance, Strategy
Schools: Ross School of Business  Class of 2017
GPA: 3.2
WE: Project Management (Other)

Re: In the figure shown, what is the value of x? [#permalink]
Show Tags
20 Jun 2014, 03:30
shorteverything wrote: Attachment: Triangle.GIF In the figure shown, what is the value of x? (1) The length of line segment QR is equal to the length of line segment RS (2) The length of line segment ST is equal to the length of line segment TU Thanks for the share...
_________________
Raves, rants and war stories of First Year MBA Students
Received an offer? Congrats! You might want to 'Negotiate the Offer'.
I'm happy to help if you wanna know about Ross & UMich, but please do not come to me with your GMAT issues or questions. And please add a bit of humor to your questions or you'll bore me to death.



Intern
Joined: 23 Aug 2014
Posts: 42
GMAT Date: 11292014

Re: In the figure shown, what is the value of x? [#permalink]
Show Tags
24 Nov 2014, 09:55
The triangle in the figure has 2 triangles and a quadrilateral in it. S1 and S2 insufficient S1+S2 Considering the toptriangle: assign 'y' to equal angles Considering the bottom triangle: assign 'z' to the equal angles x+y+z= 180.............I Considering the quadrilateral now: 90+(180z)+x+(180y)=360 xyz=90................II Adding I and II gives me a value for x (in the spirit of seeing things through 2x=90 > x=90/2=45)



Intern
Joined: 13 Mar 2015
Posts: 3

Re: In the figure shown, what is the value of x? [#permalink]
Show Tags
16 Mar 2015, 04:40
How do I know it is not actually equilateral?



Math Expert
Joined: 02 Sep 2009
Posts: 39673

Re: In the figure shown, what is the value of x? [#permalink]
Show Tags
16 Mar 2015, 05:20




Re: In the figure shown, what is the value of x?
[#permalink]
16 Mar 2015, 05:20



Go to page
1 2
Next
[ 36 posts ]





Similar topics 
Author 
Replies 
Last post 
Similar Topics:


18


In the parallelogram shown, what is the value of x?

Bunuel 
6 
06 Jan 2017, 00:46 

21


In the figure above, what is the value of x?

emmak 
7 
27 Nov 2015, 11:19 



In the figure shown, what is the value of x?

thagem01 
5 
08 Aug 2012, 15:15 

10


In the figure shown, what is the value of x?

sdrandom1 
8 
09 May 2014, 03:16 

9


In the figure shown, what is the value of x?

CasperMonday 
6 
13 Jun 2017, 23:12 



