Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 28 Feb 2012
Posts: 27

You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]
Show Tags
02 Jun 2012, 09:22
2
This post received KUDOS
7
This post was BOOKMARKED
Question Stats:
42% (02:39) correct
58% (01:43) wrong based on 183 sessions
HideShow timer Statistics
You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 centimeters. The number of noncongruent triangles that can be formed by choosing three of the sticks to make the sides is A. 3 B. 6 C. 7 D. 10 E. 12 OA will be posted after some time. Please inclease my Kudos if you like the problem...
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 02 Jun 2012, 12:45, edited 1 time in total.
Edited the question and added the OA



Math Expert
Joined: 02 Sep 2009
Posts: 39662

Re: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]
Show Tags
02 Jun 2012, 12:49
sandal85 wrote: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 centimeters. The number of noncongruent triangles that can be formed by choosing three of the sticks to make the sides is
A. 3 B. 6 C. 7 D. 10 E. 12
OA will be posted after some time.
Please inclease my Kudos if you like the problem... The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.Based on this there can be only 7 triangles formed: (20, 30, 40), (20, 40, 50), (20, 50, 60), (30, 40, 50), (30, 40, 60), (30, 50, 60), (40, 50, 60). Answer; C.
_________________
New to the Math Forum? Please read this: 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



Director
Joined: 24 Aug 2009
Posts: 503
Schools: Harvard, Columbia, Stern, Booth, LSB,

Re: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]
Show Tags
07 Sep 2012, 12:12
Bunuel wrote: sandal85 wrote: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 centimeters. The number of noncongruent triangles that can be formed by choosing three of the sticks to make the sides is
A. 3 B. 6 C. 7 D. 10 E. 12
OA will be posted after some time.
Please inclease my Kudos if you like the problem... The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.Based on this there can be only 7 triangles formed: (20, 30, 40), (20, 40, 50), (20, 50, 60), (30, 40, 50), (30, 40, 60), (30, 50, 60), (40, 50, 60). Answer; C. Hi Bunuel, Is there any other method (combinatorics) to solve this question ?
_________________
If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth Game Theory
If you have any question regarding my post, kindly pm me or else I won't be able to reply



Manager
Joined: 24 Jul 2011
Posts: 76
Location: India
Concentration: Strategy, General Management
WE: Asset Management (Manufacturing)

Re: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]
Show Tags
09 Sep 2012, 04:32
fameatop wrote: Hi Bunuel,
Is there any other method (combinatorics) to solve this question ?
Following method may be applied As Bunuel has mentioned "The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides."This a very important characteristic of triangle. [Thanks Bunuel, you are genius !!! ] Now coming to this particular problem, we have sides mentioned as 10, 20, 30, 40, 50, 60. Difference between any tow sides is 10, therefore 10 cannot be any side of a triangle. So, we are left with 20, 30, 40, 50 and 60. >> 5 sides. Now, Number of triangles can be formed with 5 sides is \(^^5C {^}3\) \(= 10\) However, following triangles are not possible \([ 20, 30, 50 ]  as 20 + 30 (NOT) > 50\) Similarly \([20, 30, 60 ]\) is not possible Similarly \([20, 40, 60]\) is not possible [Note: Easiest way to eliminate triangles is to start with least two sides and sum them up. All the sides having equal or higher that value are eliminated. In our case we started with 20 and 30. Hence, 50, and 60 are eliminated. Repeat the same process with the next number along with the least one. In our case 20 and 40. So, 40 is eliminated. ]So, finally the number of triangles is \(103 =7\) Hope, this is more logical and quicker method of solving such problem.
_________________
My mantra for cracking GMAT: Everyone has inborn talent, however those who complement it with hard work we call them 'talented'.
+1 Kudos = Thank You Dear Are you saying thank you?



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15958

Re: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]
Show Tags
18 May 2014, 09:25
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



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15958

Re: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]
Show Tags
18 Oct 2015, 07:43
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



Manager
Joined: 02 Nov 2014
Posts: 215
GMAT Date: 08042015

Re: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]
Show Tags
07 Dec 2015, 01:53
Got this correct but spent 3.48 Used trial and error, keeping the basic properties of triangle in mind. Anybody has a better / faster method?? Thanks.



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15958

Re: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]
Show Tags
14 Apr 2017, 08:40
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: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60
[#permalink]
14 Apr 2017, 08:40








Similar topics 
Author 
Replies 
Last post 
Similar Topics:


1


Let A=6^20, B=2^60, and C=4^50. Which of the following is true?

MathRevolution 
4 
08 Mar 2017, 01:41 

2


how many trailing zero's in N = (5^5*10^5*15^5*20^5*25^5*30^5*35^5*40)

yezz 
6 
21 Jan 2017, 14:42 

4


IF N = 5*10*15*20*25*30*35*40*45*50 , trailing zero's??

yezz 
1 
11 Jan 2017, 03:47 

5


The average of 20, 60 and 180 is twice the average of 10, 30, and whic

alanforde800Maximus 
6 
22 Dec 2016, 09:42 

7


Of 60 children, 30 are happy, 10 are sad, and 20 are neither

langtuprovn2007 
6 
20 Oct 2016, 08:52 



