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 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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

\(x+\angle{QSR}+\angle{UST}=180\) (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.

Re: Help me with this triangle geometry DS [#permalink]

Show Tags

05 Nov 2010, 17:32

2

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 = (180-ASRQ)/2 From statement 2: we know that ATSU = (180-ASTU)/2

Plugging these information into the x = 180 - ARSQ - ATSU we see that

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=180-2j and that z=180-2k. Finally, we have that w+z=90 or that (180-2j)+(180-2k)=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/massive-collection-of-verbal-questions-sc-rc-and-cr-106195.html#p832142

[highlight]Massive collection of thousands of Data Sufficiency and Problem Solving questions and answers:[/highlight] http://gmatclub.com/forum/1001-ds-questions-file-106193.html#p832133

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=180-2j and that z=180-2k. Finally, we have that w+z=90 or that (180-2j)+(180-2k)=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.
_________________

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/massive-collection-of-verbal-questions-sc-rc-and-cr-106195.html#p832142

[highlight]Massive collection of thousands of Data Sufficiency and Problem Solving questions and answers:[/highlight] http://gmatclub.com/forum/1001-ds-questions-file-106193.html#p832133

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".
_________________

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=(180-R)/2 (as <PQS+<QSR+<R=180 --> 2<QSR+<R=180 --> <QSR=(180-R)/2). Not sufficient.

(2) The legnth of line segment ST is equal to the length of line segment TU --> UST is isosceles --> <SUT=<UST=(180-T)/2. Not sufficient.

Two equations, x = 180 - (a + b), where a and b are RQS and SUT. x = 360 -[(180-a) + (180-b) + 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 = 3-4 min

Re: In the figure shown, what is the value of x? [#permalink]

Show Tags

08 Aug 2012, 14:37

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 90-60-30 or 90-45-45 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 90-60-30: <RST + <TSU = 135 degree, so X =45 degree For 90-45-45: <RST + <TSU = 135/2 + 135/2 = 135 Degree, so X =45 Degree
_________________

Regards SD ----------------------------- Press Kudos if you like my post. Debrief 610-540-580-710(Long Journey): http://gmatclub.com/forum/from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html

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 -(180-x) = 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?

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.

Re: In the figure shown, what is the value of x? [#permalink]

Show Tags

24 Nov 2014, 08:55

The triangle in the figure has 2 triangles and a quadrilateral in it. S1 and S2 insufficient S1+S2 Considering the top-triangle: 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+(180-z)+x+(180-y)=360 x-y-z=-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)

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...