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In the figure shown, what is the value of x? [#permalink]
 25 Jul 2010, 20:24
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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 legnth of line segment ST is equal to the length of line segment TU Attachment: 
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Re: GMAT Prep Question... plz explain??? [#permalink]
26 Jul 2010, 14:56
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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 --> <RQS=<QSR=(180-R)/2 (as <RQS+<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. (1)+(2) x+<QSR+<UST=180 --> x+(180-R)/2+(180-T)/2=180 --> x+(360-(R+T))/2=180 --> as R+T=90 --> x+(360-90)/2=180 --> x=45. Sufficient. Answer: C.
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Re: Help me with this triangle geometry DS [#permalink]
05 Nov 2010, 18:32
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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
x = 180 - (180-ASRQ)/2 - (180-ASTU)/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.
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Re: Help me with this triangle geometry DS [#permalink]
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
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GMAT Prep DS, geometry: Find angle X [#permalink]
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=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!
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Re: GMAT Prep DS, geometry: Find angle X [#permalink]
20 Dec 2010, 15:11
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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=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.
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Re: GMAT Prep Question... plz explain??? [#permalink]
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!
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Re: GMAT Prep Question... plz explain??? [#permalink]
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".
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Re: GMAT Prep Question... plz explain??? [#permalink]
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=(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. (1)+(2) x+<QSR+<UST=180 --> x+(180-R)/2+(180-T)/2=180 --> x+(360-(R+T))/2=180 --> as R+T=90 --> x+(360-90)/2=180 --> x=45. Sufficient. Answer: C. so kool 
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Re: GMAT Prep Question... plz explain??? [#permalink]
16 Mar 2011, 21:19
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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 -(180-x) = 0 => 2x - 90 = 0 => x = 45 So the answer is C.
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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
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C it is. 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.
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Re: In the figure shown, what is the value of x? [#permalink]
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 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
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What is the value of x? [#permalink]
22 Sep 2012, 06:34
In the attached figure what is the value of x?
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Screenshot02 22-Sep-12 21.28.jpg [ 5.39 KiB | Viewed 3800 times ]
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What is the value of angle x? [#permalink]
19 Nov 2012, 10:06
In the right angle triangle with right angle at vertex A, find value of x a) CP=CQ b) BQ=BR I got this in GMAT Prep test but wasn't able to check the answer. Application closed suddenly and it didnot give me an option to review my wrong answers again. Since I am not able to get the exact vocabulary of the question, I wasn't able to search. Thanks.
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What is the value of X? [#permalink]
24 Nov 2012, 16:48
 The answer is C. Could someone please explain the theory behind this? I keep getting these types of geometry problems incorrect  _________________
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Re: What is the value of X? [#permalink]
24 Nov 2012, 16:51
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Re: What is the value of X?
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24 Nov 2012, 16:51
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