NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 13:55 It is currently 25 Apr 2024, 13:55
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
smily_buddy
Intern
Intern
Joined: 30 Jan 2006
Posts: 37
Own Kudos [?]: 126 [77]
Given Kudos: 0
Send PM
In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4 [#permalink] New post   Updated on: 14 Aug 2017, 09:10
5
Kudos
72
Bookmarks
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

72% (01:16) correct 28% (01:31) wrong based on 1274 sessions
Hide Show timer Statistics

In the triangle above, is x > 90?

(1) a^2 + b^2 <15
(2) c > 4

Show Spoiler
Attachment:
triangle.GIF
triangle.GIF [ 1.66 KiB | Viewed 24705 times ]
ShowHide Answer
Official Answer
C

Originally posted by smily_buddy on 17 Aug 2007, 13:09.
Last edited by Bunuel on 14 Aug 2017, 09:10, edited 3 times in total.
Edited the question, added the diagram and added the OA
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619011 [64]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4 [#permalink] New post   09 Feb 2012, 03:57
24
Kudos
39
Bookmarks
Expert Reply

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 \(a^2+b^2=c^2\), since \(a^2+b^2<15<(16=c^2)\) 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.

P.S. If the lengths of the sides of a triangle are a, b, and c, where the largest side is c, then:

For a right triangle: \(a^2 +b^2= c^2\).
For an acute (a triangle that has all angles less than 90°) triangle: \(a^2 +b^2>c^2\).
For an obtuse (a triangle that has an angle greater than 90°) triangle: \(a^2 +b^2<c^2\).
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619011 [6]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4 [#permalink] New post   17 Feb 2012, 02:42
3
Kudos
3
Bookmarks
Expert Reply
SergeNew wrote:
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.


If c^2 were equal to a^2+b^2 then we would have a^2+b^2=c^2, which would mean that angle x is 90 degrees. Now, since c^2 is more than a^2+b^2, then angle x, which is opposite c, must be more than 90 degrees: try to increase side c and you'll notice that angle x will increase too.

Hope it's clear.
General Discussion
avatar
SergeNew
Intern
Intern
Joined: 02 Jan 2011
Posts: 7
Own Kudos [?]: 111 [0]
Given Kudos: 0
Send PM
Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4 [#permalink] New post   17 Feb 2012, 00:26
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.
avatar
fozzzy
Director
Director
Joined: 29 Nov 2012
Posts: 580
Own Kudos [?]: 6042 [0]
Given Kudos: 543
Send PM
Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4 [#permalink] New post   26 Jan 2013, 21:15
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?
User avatar
Vips0000
Current Student
Joined: 15 Sep 2012
Status:Done with formalities.. and back..
Posts: 525
Own Kudos [?]: 1187 [0]
Given Kudos: 23
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE:Information Technology (Computer Software)
Send PM
GMAT ToolKit User Reviews Badge
Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4 [#permalink] New post   26 Jan 2013, 21:50
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)
User avatar
B
mau5
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 485
Own Kudos [?]: 3092 [2]
Given Kudos: 141
Send PM
Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4 [#permalink] New post   28 Jan 2013, 23:31
1
Kudos
1
Bookmarks
Just a handy tool to prove that the answer is C.

c^2 = a^2+b^2-2abCos(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^2-c^2 <0

a^2+b^2-c^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!
User avatar
greatps24
Manager
Manager
Joined: 22 Nov 2010
Posts: 202
Own Kudos [?]: 497 [1]
Given Kudos: 75
Location: India
GMAT 1: 670 Q49 V33
WE:Consulting (Telecommunications)
Send PM
Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4 [#permalink] New post   24 Feb 2013, 21:46
1
Bookmarks
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.
User avatar
B
longhaul123
Manager
Manager
Joined: 03 Jul 2017
Status:IF YOU CAN DREAM IT, YOU CAN DO IT
Posts: 147
Own Kudos [?]: 33 [0]
Given Kudos: 27
Location: India
Concentration: Finance, International Business
Send PM
Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4 [#permalink] New post   28 Jul 2017, 10:03
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
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619011 [0]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4 [#permalink] New post   29 Jul 2017, 01:49
Expert Reply
longhaul123 wrote:
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


How does a^2 + b^2 < 15 imply that x is not 90 degrees? We are given that the sum of the square of the lengths of two sides is less than some number. We cannot deduce anything from this. If a = b = 1 and \(c = \sqrt{2}\), then \(a^2 + b^2 = c^2\), which will make x equal to 90 degrees but if a = b = c = 1, then x will be equal to 60 degrees.
User avatar
G
Basshead
Director
Director
Joined: 09 Jan 2020
Posts: 966
Own Kudos [?]: 223 [2]
Given Kudos: 434
Location: United States
Send PM
In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4 [#permalink] New post   19 Nov 2020, 07:56
2
Kudos
smily_buddy wrote:

In the triangle above, is \(x > 90\)?

(1)\( a^2 + b^2 <15\)
(2) c > 4

Show Spoiler
Attachment:
triangle.GIF


(1) a = b = c = 1; each side would be 60 degrees.
a = b = 1 and c = 2; in this case x > 90.

INSUFFICIENT.

(2) No information about either a or b; INSUFFICIENT.

(1) We know \(a^2 + b^2 < 15\) and \(c > 4\)

\(c^2 > 16\)

\(a^2 + b^2 < 15 < c^2\)

x is greater than 90 degrees. SUFFICIENT.

Answer is C.
User avatar
B
dsteeps
Intern
Intern
Joined: 24 Jul 2019
Posts: 5
Own Kudos [?]: 1 [0]
Given Kudos: 3
Send PM
Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4 [#permalink] New post   31 Dec 2022, 13:49
Very good question! Thanks for posting.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32679
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4 [#permalink] New post   07 Jan 2024, 03:55
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 Club Bot
gmatclubot
Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4 [#permalink]
07 Jan 2024, 03:55
Moderator:
Bunuel
Math Expert
92915 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions