December 14, 2018 December 14, 2018 10:00 PM PST 11:00 PM PST Carolyn and Brett  nicely explained what is the typical day of a UCLA student. I am posting below recording of the webinar for those who could't attend this session. December 15, 2018 December 15, 2018 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51215

Triangle QSR is inscribed in a circle. Is QSR a right triangle?
[#permalink]
Show Tags
14 Apr 2017, 02:52
Question Stats:
68% (00:35) correct 32% (00:34) wrong based on 158 sessions
HideShow timer Statistics



Director
Joined: 21 Mar 2016
Posts: 521

Triangle QSR is inscribed in a circle. Is QSR a right triangle?
[#permalink]
Show Tags
Updated on: 14 Apr 2017, 06:57
stat1 : QR is a diameter... hence traingle in semicircle is right traingle suff
stat 2 : not suff... the third side cud be anything
ans A
Originally posted by mohshu on 14 Apr 2017, 06:24.
Last edited by mohshu on 14 Apr 2017, 06:57, edited 1 time in total.



VP
Joined: 05 Mar 2015
Posts: 1004

Triangle QSR is inscribed in a circle. Is QSR a right triangle?
[#permalink]
Show Tags
14 Apr 2017, 06:43
mohshu wrote: stat1 : QR is a diameter... hence traingle in semicircle is right traingle suff
stat 2 : pythagoras theorem applies here and its true only for right trangles
ans D mohshufor option (2) what if SR =4.5 ??? thanks



Director
Joined: 21 Mar 2016
Posts: 521

Re: Triangle QSR is inscribed in a circle. Is QSR a right triangle?
[#permalink]
Show Tags
14 Apr 2017, 06:56
rohit8865 wrote: mohshu wrote: stat1 : QR is a diameter... hence traingle in semicircle is right traingle suff
stat 2 : pythagoras theorem applies here and its true only for right trangles
ans D mohshufor option (2) what if SR =4.5 ??? thanks rohit8865 got that only stat is suff ans A thanks



Retired Moderator
Joined: 04 Aug 2016
Posts: 500
Location: India
Concentration: Leadership, Strategy
GPA: 4
WE: Engineering (Telecommunications)

Re: Triangle QSR is inscribed in a circle. Is QSR a right triangle?
[#permalink]
Show Tags
14 Apr 2017, 07:17
Statement 1 is a property and it is sufficient
Statement 2 : The other side can take any value between 2 and 8; if it is 4 then it is sufficient. Not enough information available.
Option A



Manager
Joined: 13 Mar 2013
Posts: 163
Location: United States
Concentration: Leadership, Technology
GPA: 3.5
WE: Engineering (Telecommunications)

Re: Triangle QSR is inscribed in a circle. Is QSR a right triangle?
[#permalink]
Show Tags
15 Apr 2017, 06:57
Ans : st 1 ) sufficient  QR is diameter . It is property of inscribed triangle in circle . If the one of the sides equal the diameter of the circle . Then the triangle is Right angle triangle . st 2 ) Not sufficient two side is given as 3 ,4 but the third side can be 5 or 7 . Apply the property of sum of two side in triangle is greater than the third side . Then you will realize . The triangle can have value as ( 3, 4, 5 > right angle ) or ( 3,4, 7 > not a right angle ) Hence A as answer . Regards, Press Kudos if you like the post.
_________________
Regards ,



Math Expert
Joined: 02 Sep 2009
Posts: 51215

Re: Triangle QSR is inscribed in a circle. Is QSR a right triangle?
[#permalink]
Show Tags
15 Apr 2017, 08:03
Bunuel wrote: Triangle QSR is inscribed in a circle. Is QSR a right triangle? (1) QR is a diameter of the circle. (2) Length QS equals 3 and length QR equals 5. Attachment: 20170414_1450.png Triangle QSR is inscribed in a semicirlce is QSR a right triangle?A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle.(1) QR is a diameter of the circle > according to the above property QSR must be a right triangle. Sufficient. (2) Length QS equals 3 and length QR equals to 5 > it's not necessary QSR to be 345 right triangle (therefor QR to be diameter/hypotenuse), for example if diameter is more than 5, say 10 than it's possible to inscribe QSR in a semicircle so that SR would be the largest side and QSR would be obtuseangled triangle. Not sufficient. Answer: A.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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
Joined: 10 Apr 2015
Posts: 182
GPA: 3.31

Re: Triangle QSR is inscribed in a circle. Is QSR a right triangle?
[#permalink]
Show Tags
15 Apr 2017, 08:39
A. II statement does not suggest that SR is 4. Hence NS. Sent from my ZUK Z2132 using GMAT Club Forum mobile app
_________________
In case you find my posts helpful, give me Kudos. Thank you.



Director
Joined: 02 Sep 2016
Posts: 681

Re: Triangle QSR is inscribed in a circle. Is QSR a right triangle?
[#permalink]
Show Tags
07 Jul 2017, 05:02
Bunuel wrote: Bunuel wrote: Triangle QSR is inscribed in a circle. Is QSR a right triangle? (1) QR is a diameter of the circle. (2) Length QS equals 3 and length QR equals 5. Attachment: 20170414_1450.png Triangle QSR is inscribed in a semicirlce is QSR a right triangle?A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle.(1) QR is a diameter of the circle > according to the above property QSR must be a right triangle. Sufficient. (2) Length QS equals 3 and length QR equals to 5 > it's not necessary QSR to be 345 right triangle (therefor QR to be diameter/hypotenuse), for example if diameter is more than 5, say 10 than it's possible to inscribe QSR in a semicircle so that SR would be the largest side and QSR would be obtuseangled triangle. Not sufficient. Answer: A. Hi BunuelIf it were 345; 3410; 645;................any multiple of 3:4:5, then it would be a right angled triangle ? Also to know if that triangle inscribed in the circle is a right triangle, then diameter would be the longest side of the triangle. Are there any other factors that can help us understand whether the triangle is a right angled triangle?



Math Expert
Joined: 02 Sep 2009
Posts: 51215

Re: Triangle QSR is inscribed in a circle. Is QSR a right triangle?
[#permalink]
Show Tags
07 Jul 2017, 05:14
Shiv2016 wrote: Bunuel wrote: Bunuel wrote: Triangle QSR is inscribed in a circle. Is QSR a right triangle? (1) QR is a diameter of the circle. (2) Length QS equals 3 and length QR equals 5. Attachment: 20170414_1450.png Triangle QSR is inscribed in a semicirlce is QSR a right triangle?A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle.(1) QR is a diameter of the circle > according to the above property QSR must be a right triangle. Sufficient. (2) Length QS equals 3 and length QR equals to 5 > it's not necessary QSR to be 345 right triangle (therefor QR to be diameter/hypotenuse), for example if diameter is more than 5, say 10 than it's possible to inscribe QSR in a semicircle so that SR would be the largest side and QSR would be obtuseangled triangle. Not sufficient. Answer: A. Hi BunuelIf it were 345; 3410; 645;................any multiple of 3:4:5, then it would be a right angled triangle ? Also to know if that triangle inscribed in the circle is a right triangle, then diameter would be the longest side of the triangle. Are there any other factors that can help us understand whether the triangle is a right angled triangle? • Any triangle whose sides are in the ratio 3:4:5 is a right triangle. Such triangles that have their sides in the ratio of whole numbers are called Pythagorean Triples. There are an infinite number of them, and this is just the smallest. If you multiply the sides by any number, the result will still be a right triangle whose sides are in the ratio 3:4:5. For example 6, 8, and 10.• A Pythagorean triple consists of three positive integers \(a\), \(b\), and \(c\), such that \(a^2 + b^2 = c^2\). Such a triple is commonly written \((a, b, c)\), and a wellknown example is \((3, 4, 5)\). If \((a, b, c)\) is a Pythagorean triple, then so is \((ka, kb, kc)\) for any positive integer \(k\). There are 16 primitive Pythagorean triples with c ≤ 100: (3, 4, 5) (5, 12, 13) (7, 24, 25) (8, 15, 17) (9, 40, 41) (11, 60, 61) (12, 35, 37) (13, 84, 85) (16, 63, 65) (20, 21, 29) (28, 45, 53) (33, 56, 65) (36, 77, 85) (39, 80, 89) (48, 55, 73) (65, 72, 97). So, 3:4:10 is not a Pythagorean triple, 3^2 + 4^2 does not equal 10^2. You'll get a Pythagorean triple if you multiply another Pythagorean triple by a positive integer, so multiply the entire ratio, not just one of its numbers.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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



NonHuman User
Joined: 09 Sep 2013
Posts: 9160

Re: Triangle QSR is inscribed in a circle. Is QSR a right triangle?
[#permalink]
Show Tags
29 Nov 2018, 08:19
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: Triangle QSR is inscribed in a circle. Is QSR a right triangle? &nbs
[#permalink]
29 Nov 2018, 08:19






