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# You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60

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Intern
Joined: 28 Feb 2012
Posts: 25
You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]

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02 Jun 2012, 08:22
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Difficulty:

85% (hard)

Question Stats:

41% (01:37) correct 59% (02:03) wrong based on 193 sessions

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You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 centimeters. The number of non-congruent 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...
[Reveal] Spoiler: OA

Last edited by Bunuel on 02 Jun 2012, 11:45, edited 1 time in total.
Edited the question and added the OA
Math Expert
Joined: 02 Sep 2009
Posts: 43361
Re: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]

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02 Jun 2012, 11:49
Expert's post
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sandal85 wrote:
You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 centimeters. The number of non-congruent 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).

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Joined: 24 Aug 2009
Posts: 492
Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]

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07 Sep 2012, 11:12
Bunuel wrote:
sandal85 wrote:
You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 centimeters. The number of non-congruent 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).

Hi Bunuel,

Is there any other method (combinatorics) to solve this question ?
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Joined: 24 Jul 2011
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Re: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]

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09 Sep 2012, 03:32
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 $$10-3 =7$$

Hope, this is more logical and quicker method of solving such problem.
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Re: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]

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18 May 2014, 08:25
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Re: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]

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18 Oct 2015, 06:43
Hello from the GMAT Club BumpBot!

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Re: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]

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07 Dec 2015, 00:53
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.
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Re: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]

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14 Apr 2017, 07:40
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).

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Re: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60   [#permalink] 14 Apr 2017, 07:40
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