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

 It is currently 22 Feb 2019, 17:13

### 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
Your Progress

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 RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
• ### FREE Quant Workshop by e-GMAT!

February 24, 2019

February 24, 2019

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Senior RC Moderator
Status: Preparing GMAT
Joined: 02 Nov 2016
Posts: 2260
Location: Pakistan
GPA: 3.39
A state has 20 cities. The train service in the state connects all cit  [#permalink]

### Show Tags

14 Oct 2018, 10:18
4
00:00

Difficulty:

45% (medium)

Question Stats:

67% (01:19) correct 33% (01:32) wrong based on 39 sessions

### HideShow timer Statistics

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

_________________

New Project RC Butler 2019 - Practice 2 RC Passages Everyday
Final days of the GMAT Exam? => All GMAT Flashcards.
This Post Helps = Press +1 Kudos
Best of Luck on the GMAT!!

Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: A state has 20 cities. The train service in the state connects all cit  [#permalink]

### Show Tags

14 Oct 2018, 17:25
SajjadAhmad 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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Manager
Joined: 16 Jun 2018
Posts: 52
Re: A state has 20 cities. The train service in the state connects all cit  [#permalink]

### Show Tags

14 Oct 2018, 21:57
1
chetan2u wrote:
SajjadAhmad 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: 7334
Re: A state has 20 cities. The train service in the state connects all cit  [#permalink]

### Show Tags

14 Oct 2018, 23:53
suelahmed wrote:
chetan2u wrote:
SajjadAhmad 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.
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Manager
Joined: 02 Aug 2015
Posts: 152
Re: A state has 20 cities. The train service in the state connects all cit  [#permalink]

### Show Tags

15 Oct 2018, 00:03
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.

If you're still not convinced, please elaborate your question.

Cheers!
Manager
Joined: 16 Jun 2018
Posts: 52
Re: A state has 20 cities. The train service in the state connects all cit  [#permalink]

### Show Tags

15 Oct 2018, 00:17
@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, 00:17
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.