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# A state has 20 cities. The train service in the state connects all cit

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Joined: 02 Nov 2016
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A state has 20 cities. The train service in the state connects all cit  [#permalink]

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14 Oct 2018, 11:18
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66% (01:20) correct 34% (01:30) wrong based on 35 sessions

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A state has 20 cities. The train service in the state connects all cities in triplets; this means that one train shall circulate only among three particular cities. To ensure that any set of three cities in the state is interconnected through a triplet, what is the minimum number of trains needed?

A. 6840
B. 2280
C. 1140
D. 570
E. 60

Source: Experts Global GMAT
Difficulty Level: 650

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Math Expert
Joined: 02 Aug 2009
Posts: 7958
Re: A state has 20 cities. The train service in the state connects all cit  [#permalink]

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14 Oct 2018, 18:25
A state has 20 cities. The train service in the state connects all cities in triplets; this means that one train shall circulate only among three particular cities. To ensure that any set of three cities in the state is interconnected through a triplet, what is the minimum number of trains needed?

A. 6840
B. 2280
C. 1140
D. 570
E. 60

EG

The question is just asking you the different ways to choose 3 cities out of 20..
So 20C3=$$\frac{20!}{(20-3)!3!}=\frac{20*19*18}{3!}$$=20*19*3=1140

C
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Re: A state has 20 cities. The train service in the state connects all cit  [#permalink]

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14 Oct 2018, 22:57
1
chetan2u wrote:
A state has 20 cities. The train service in the state connects all cities in triplets; this means that one train shall circulate only among three particular cities. To ensure that any set of three cities in the state is interconnected through a triplet, what is the minimum number of trains needed?

A. 6840
B. 2280
C. 1140
D. 570
E. 60

EG

The question is just asking you the different ways to choose 3 cities out of 20..
So 20C3=$$\frac{20!}{(20-3)!3!}=\frac{20*19*18}{3!}$$=20*19*3=1140

C

Wouldn't be it 3! * 1140. Since a train can have 6 ways between stations ?
Math Expert
Joined: 02 Aug 2009
Posts: 7958
Re: A state has 20 cities. The train service in the state connects all cit  [#permalink]

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15 Oct 2018, 00:53
suelahmed wrote:
chetan2u wrote:
A state has 20 cities. The train service in the state connects all cities in triplets; this means that one train shall circulate only among three particular cities. To ensure that any set of three cities in the state is interconnected through a triplet, what is the minimum number of trains needed?

A. 6840
B. 2280
C. 1140
D. 570
E. 60

EG

The question is just asking you the different ways to choose 3 cities out of 20..
So 20C3=$$\frac{20!}{(20-3)!3!}=\frac{20*19*18}{3!}$$=20*19*3=1140

C

Wouldn't be it 3! * 1140. Since a train can have 6 ways between stations ?

No it will not be..
Firstly question asks for number of trains that connect three stations as a triplet. So we are looking at selection of three cities and not arrangements.
Secondly Minimum number of trains should get you thinking. Min number along with the way question is formed clearly vtells you it is combinations question.
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Posts: 153
Re: A state has 20 cities. The train service in the state connects all cit  [#permalink]

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15 Oct 2018, 01:03
suelahmed wrote:
Wouldn't be it 3! * 1140. Since a train can have 6 ways between stations ?

Hey suelahmed,

Question asked: Minimum no.of trains required. Let's say each triplet requires 1 train.

To find: No.of triplets out of 20 cities so that each triplet has its own train.

No of triplets - 1140. So there are 1140 trains running.

Cheers!
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Joined: 16 Jun 2018
Posts: 50
Re: A state has 20 cities. The train service in the state connects all cit  [#permalink]

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15 Oct 2018, 01:17
@Diwakar002, chetan2u

Got it.. i got confused with min number of train that train could travel between 20 stations.

thanks a lot
Re: A state has 20 cities. The train service in the state connects all cit   [#permalink] 15 Oct 2018, 01:17
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