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Teddy has a set of dowels, each with a distinct length in centimeters,

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Teddy has a set of dowels, each with a distinct length in centimeters, [#permalink]

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Teddy has a set of dowels, each with a distinct length in centimeters, represented by a prime number. If Teddy can create twenty-three distinct triangles using as many dowels as is necessary for each triangle, what is the least possible value of the longest dowel?

(A) 7
(B) 11
(C) 13
(D) 17
(E) 23
[Reveal] Spoiler: OA

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Re: Teddy has a set of dowels, each with a distinct length in centimeters, [#permalink]

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New post 24 Sep 2017, 01:58
Could someone rectify me?

If we have 23 different triangles than the number of dowels we need can be found through solving for n the following equation:

nC3 = 23; or n*(n-1)*(n-2)=2*3*23; but it is impossible to do in integer numbers.
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Re: Teddy has a set of dowels, each with a distinct length in centimeters, [#permalink]

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New post 01 Oct 2017, 03:04
i tried to follow the pattern

1,3,5,7--- 4c3 out of 4 only one is valid triangle with sides 3,5,7
1,3,5,7,11 5c3 out of 10 only 2 are valid triangles 3,5,7 5,7,11
1,3,5,7,11,13 out of 6c3 only 4 valid tangles 3,5,7 5,7,11 3,11,13 5,11,13


if we follow this pattren

with 4 prime nos we get one valid trangle

4---1
5---2
6---4
7---8
8---16 here at when one no is 23 we get 16 valid trangle
now at 9---(means 29) we get 32 valid trangles , which should be the ans and not an option..



BUNUEL please suggest..
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Re: Teddy has a set of dowels, each with a distinct length in centimeters, [#permalink]

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New post 09 Oct 2017, 12:14
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Bunuel wrote:
Teddy has a set of dowels, each with a distinct length in centimeters, represented by a prime number. If Teddy can create twenty-three distinct triangles using as many dowels as is necessary for each triangle, what is the least possible value of the longest dowel?

(A) 7
(B) 11
(C) 13
(D) 17
(E) 23


Say, we take 2,3,5 and 7.
Then we can create 4C3 + 4*3 (two times 2 and other 3 numbers+two times 3 and other 3 numbers ...) = 4+12 =16

If we take 2,3,5,7,11.
Then we can create 5C3 + 5*4 = 10+20= 30. Which is sufficient.

Thus answer is (B) 11.

Correct me if I am wrong.
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Re: Teddy has a set of dowels, each with a distinct length in centimeters, [#permalink]

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New post 10 Nov 2017, 09:39
VeritasPrepKarishma please share an approach for this.
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Re: Teddy has a set of dowels, each with a distinct length in centimeters, [#permalink]

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New post 11 Nov 2017, 20:37
HI

4C3 + 4*3 , why hav u included 4*3 here...
even I m getting 4C3, but what is this 4*3?


anirudsuhag.25 wrote:
Bunuel wrote:
Teddy has a set of dowels, each with a distinct length in centimeters, represented by a prime number. If Teddy can create twenty-three distinct triangles using as many dowels as is necessary for each triangle, what is the least possible value of the longest dowel?

(A) 7
(B) 11
(C) 13
(D) 17
(E) 23


Say, we take 2,3,5 and 7.
Then we can create 4C3 + 4*3 (two times 2 and other 3 numbers+two times 3 and other 3 numbers ...) = 4+12 =16

If we take 2,3,5,7,11.
Then we can create 5C3 + 5*4 = 10+20= 30. Which is sufficient.

Thus answer is (B) 11.

Correct me if I am wrong.

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Re: Teddy has a set of dowels, each with a distinct length in centimeters,   [#permalink] 11 Nov 2017, 20:37
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