GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Feb 2019, 16:03

### 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

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

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT Algebra Webinar

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.
• ### Free GMAT Strategy Webinar

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.

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

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
3
23
00:00

Difficulty:

35% (medium)

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 ]

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.
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
16
21

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).

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: $$a^2 +b^2<c^2$$.
_________________
##### General Discussion
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: 04-23-2012
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
2
1
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.
_________________
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).

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).

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
1
1
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!
_________________
Manager
Joined: 22 Nov 2010
Posts: 221
Location: India
GMAT 1: 670 Q49 V33
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
1
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
GMAT 1: 700 Q49 V38
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.
Manager
Status: IF YOU CAN DREAM IT, YOU CAN DO IT
Joined: 03 Jul 2017
Posts: 196
Location: India
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
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.
_________________
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/abc-with-a-t ... l#p1041826

Hope it helps.
_________________
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
cocojatti92 wrote:
Hello Quick question
Can the ans be A
Im a little confused

The correct answer is C. Check here: https://gmatclub.com/forum/abc-with-a-t ... l#p1041826
_________________
Non-Human 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.
_________________
Re: In the triangle above, is x > 90? (1) a^2 + b^2 < 15 (2) c>4   [#permalink] 09 Dec 2018, 16:13
Display posts from previous: Sort by