February 17, 2019 February 17, 2019 07:00 AM PST 09:00 AM PST Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT. February 16, 2019 February 16, 2019 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

Manager
Joined: 30 Jan 2006
Posts: 60

In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4
[#permalink]
Show Tags
Updated on: 14 Aug 2017, 08:10
Question Stats:
67% (01:22) correct 33% (01:33) wrong based on 797 sessions
HideShow timer Statistics
In the triangle above, is x > 90? (1) a^2 + b^2 <15 (2) c > 4 Attachment:
triangle.GIF [ 1.66 KiB  Viewed 5027 times ]
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by smily_buddy on 17 Aug 2007, 12:09.
Last edited by Bunuel on 14 Aug 2017, 08:10, edited 3 times in total.
Edited the question, added the diagram and added the OA




Math Expert
Joined: 02 Sep 2009
Posts: 52902

In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4
[#permalink]
Show Tags
09 Feb 2012, 02:57




Intern
Joined: 02 Jan 2011
Posts: 9

Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4
[#permalink]
Show Tags
16 Feb 2012, 23:26
Quote: c^2 is greater than a^2+b^2 then the angel opposite c must be greater than 90 Hi Guys, Would anyone be able to explain why the angle is greater than 90 if c^2 is greater than a^2+b^2? Serge.



Intern
Joined: 16 Dec 2011
Posts: 40
GMAT Date: 04232012

Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4
[#permalink]
Show Tags
17 Feb 2012, 01:27
Whenever Asqr + Bsqr Is equal to Csqr than angle X is 90 degrees Look at both options carefully ,
Asqr + Bsqr Is less than 15 and C greater than 4 means any value more than 4 for c and will automatically increase angle X bcoz as C increases angle 8 increases
Poor in making posts
Hope it will help.
Posted from my mobile device



Math Expert
Joined: 02 Sep 2009
Posts: 52902

Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4
[#permalink]
Show Tags
17 Feb 2012, 01:42



Director
Joined: 29 Nov 2012
Posts: 749

Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4
[#permalink]
Show Tags
26 Jan 2013, 20:15
Bunuel wrote: I attached the diagram, which was missing in initial post. Attachment: Trianlge.PNG In the triangle above, is x > 90?(1) a^2 + b^2 <15 (2) c > 4 Each statement alone is clearly insufficient. When taken together: If angle x were 90 degrees than we would have a^2+b^2=4^2, since a^2+b^2<15<16 then angle x must be greater than 90 degrees (c^2 is greater than a^2+b^2 then the angel opposite c must be greater than 90). Answer: C. Hope it helps. What would happen is the statement was c>3? how would this question be framed such that the angle could be always below 90 degrees. Since in this particular question the solution will always be greater, what would be the opposite case?



Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 587
Location: India
Concentration: Strategy, General Management
Schools: Olin  Wash U  Class of 2015
WE: Information Technology (Computer Software)

Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4
[#permalink]
Show Tags
26 Jan 2013, 20:50
fozzzy wrote: Bunuel wrote: I attached the diagram, which was missing in initial post. Attachment: Trianlge.PNG In the triangle above, is x > 90?(1) a^2 + b^2 <15 (2) c > 4 Each statement alone is clearly insufficient. When taken together: If angle x were 90 degrees than we would have a^2+b^2=4^2, since a^2+b^2<15<16 then angle x must be greater than 90 degrees (c^2 is greater than a^2+b^2 then the angel opposite c must be greater than 90). Answer: C. Hope it helps. What would happen is the statement was c>3? how would this question be framed such that the angle could be always below 90 degrees. Since in this particular question the solution will always be greater, what would be the opposite case? If you reverse the values, such as: (1) a^2 + b^2 >16 (2) c < 4 You would get a case where angle x would be less than 90, provided a triangle is still formed. (Note that a+b will tend to be bigger and C tends to be smaller in this option)
_________________
Lets Kudos!!! Black Friday Debrief



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 611

Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4
[#permalink]
Show Tags
28 Jan 2013, 22:31
Just a handy tool to prove that the answer is C. c^2 = a^2+b^22abCos(c). In this case , Angle c = x. Now, we know that c^2 >16 Also, a^+b^2<15. Thus a^2+b^2<c^2 = a^2+b^2c^2 <0 a^2+b^2c^2 = 2abCos(x) ; 2abCos(x) <0. As ab!=0,Cos(x)<0. Thus, X>90 degree. For c=90 degree, the above equality gives the famous theorem!
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Manager
Joined: 22 Nov 2010
Posts: 221
Location: India
WE: Consulting (Telecommunications)

Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4
[#permalink]
Show Tags
24 Feb 2013, 20:46
smily_buddy wrote: Attachment: Trianlge.PNG In the triangle above, is x > 90? (1) a^2 + b^2 <15 (2) c > 4 If a^2 + b^2 = c^2 then x= 90. But , as given in st2, minimum value of C = 5, then C^2 = 25. It means a^2 + b^2 < c^2.Thus, x <90. Therefore, C.
_________________
YOU CAN, IF YOU THINK YOU CAN



Intern
Joined: 16 Jan 2013
Posts: 22

Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4
[#permalink]
Show Tags
24 Feb 2013, 22:14
abhi47 wrote: E is the correct answer. Both statements are insufficient. from one, possible values of (a,b) = (1,2) or (1,3) or (2,3) or (2,2) from 2nd, given that c>4 Property of triangle is = sum of two sides > third side therefor only possible values are a= 2, b=3 and c = 5 or a = 3 and b = 2 and c =5 since a^2 + b ^2 = c^2 hence it is a right angle triangle hence both conditions required to answer so option(c)



Current Student
Joined: 06 Apr 2015
Posts: 14
Location: United States (NY)
Concentration: Technology, Finance

Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4
[#permalink]
Show Tags
01 Oct 2015, 16:41
a^2+b^2 = c^2 then angle opposite of c is right angle triangle a^2+b^2 < c^2 then angle opposite of c is greater than 90 a^2+b^2 > c^2 then angle opposite of c is less than 90
Using the above logic, we can make of use of both the statements to answer the question. Hence answer is C.



Manager
Status: IF YOU CAN DREAM IT, YOU CAN DO IT
Joined: 03 Jul 2017
Posts: 196
Location: India
Concentration: Finance, International Business

Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4
[#permalink]
Show Tags
28 Jul 2017, 09:03
The inequality a^2+b^2,15 shows that the angle x is not equal to 90 so it can lesser or greater. So the statement 1 is sufficient. I know that i have some mistake with the concept, can someone please correct me. thank you



Intern
Joined: 07 Jun 2017
Posts: 20

Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4
[#permalink]
Show Tags
29 Jul 2017, 00:10
jbisht wrote: abhi47 wrote: E is the correct answer. Both statements are insufficient. from one, possible values of (a,b) = (1,2) or (1,3) or (2,3) or (2,2) from 2nd, given that c>4 Property of triangle is = sum of two sides > third side therefor only possible values are a= 2, b=3 and c = 5 or a = 3 and b = 2 and c =5 since a^2 + b ^2 = c^2 hence it is a right angle triangle hence both conditions required to answer so option(c) How can sum of two sides be equal to third side in your argument above where a=2,b=3 and c=5, if this triangle is drawn will it not be a single line ? IMO E is the correct answer



Math Expert
Joined: 02 Sep 2009
Posts: 52902

Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4
[#permalink]
Show Tags
29 Jul 2017, 00:49



Math Expert
Joined: 02 Sep 2009
Posts: 52902

Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4
[#permalink]
Show Tags
29 Jul 2017, 00:49
saurabhSuman wrote: jbisht wrote: abhi47 wrote: E is the correct answer. Both statements are insufficient. from one, possible values of (a,b) = (1,2) or (1,3) or (2,3) or (2,2) from 2nd, given that c>4 Property of triangle is = sum of two sides > third side therefor only possible values are a= 2, b=3 and c = 5 or a = 3 and b = 2 and c =5 since a^2 + b ^2 = c^2 hence it is a right angle triangle hence both conditions required to answer so option(c) How can sum of two sides be equal to third side in your argument above where a=2,b=3 and c=5, if this triangle is drawn will it not be a single line ? IMO E is the correct answer The correct answer is C. Check here: https://gmatclub.com/forum/abcwithat ... l#p1041826Hope it helps.
_________________
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



Intern
Joined: 28 Aug 2016
Posts: 6

Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4
[#permalink]
Show Tags
30 Nov 2017, 15:46
Hello Quick question Can the ans be A Im a little confused



Math Expert
Joined: 02 Sep 2009
Posts: 52902

Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4
[#permalink]
Show Tags
30 Nov 2017, 19:58



NonHuman User
Joined: 09 Sep 2013
Posts: 9839

Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4
[#permalink]
Show Tags
09 Dec 2018, 16:13
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: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4
[#permalink]
09 Dec 2018, 16:13






