Last visit was: 23 Apr 2026, 05:56 It is currently 23 Apr 2026, 05:57
Home
Messages
Tests
Schools
Events
Close
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,778
Own Kudos:
810,772
 [26]
Given Kudos: 105,853
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,778
Kudos: 810,772
 [26]
A state has 20 cities. The train service in the state connects all cit 03 Sep 2021, 04:23
2
Kudos
Add Kudos
24
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

67% (01:35) correct 33% (01:59) wrong based on 362 sessions

History

Date
Time
Result
Not Attempted Yet
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
ShowHide Answer
Official Answer
C
User avatar
CrackverbalGMAT
User avatar
Major Poster
Joined: 03 Oct 2013
Last visit: 22 Apr 2026
Posts: 4,846
Own Kudos:
9,181
 [1]
Given Kudos: 226
Affiliations: CrackVerbal
Location: India
Expert
Expert reply
Posts: 4,846
Kudos: 9,181
 [1]
A state has 20 cities. The train service in the state connects all cit 03 Sep 2021, 05:29
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
This question can be easily solved by using the concept of Combination
The minimum number of trains needed is same as no of ways you can select 3 cities out of 20 = 20 C 3 = (20* 19* 18)/3! = (20* 19* 18)/6= 20 * 19 * 3 = 1140

Option C is the correct answer.

Thanks,
Clifin J Francis,
GMAT SME
avatar
magic73
avatar
Joined: 09 Sep 2021
Last visit: 09 Sep 2021
Posts: 1
Own Kudos:
1
 [1]
Posts: 1
Kudos: 1
 [1]
A state has 20 cities. The train service in the state connects all cit 09 Sep 2021, 11:41
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
CrackverbalGMAT
This question can be easily solved by using the concept of Combination
The minimum number of trains needed is same as no of ways you can select 3 cities out of 20 = 20 C 3 = (20* 19* 18)/3! = (20* 19* 18)/6= 20 * 19 * 3 = 1140

Option C is the correct answer.

Thanks,
Clifin J Francis,
GMAT SME
Show more

I don't think C is correct. It should not be a combination. Consider the case with 4 cities instead of 20. 4c3 equals 4. However, you can cover 4 cities using just 3 triplets - ABC, BCD and ACD. Similarly, 6 cities can be covered in less than 6C3 (I have found a solution where 6 cities can be covered in 6 triplets).

Posted from my mobile device
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 23 Apr 2026
Posts: 5,986
Own Kudos:
5,858
 [2]
Given Kudos: 163
Location: India
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
My Reviews
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
Posts: 5,986
Kudos: 5,858
 [2]
A state has 20 cities. The train service in the state connects all cit 09 Sep 2021, 11:46
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Given: 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.

Asked: To ensure that any set of three cities in the state is interconnected through a triplet, what is the minimum number of trains needed?

Minimum number of trains needed = 20C3 = 1140

IMO C
User avatar
aditijain1507
User avatar
Joined: 16 Nov 2021
Last visit: 28 Feb 2024
Posts: 47
Own Kudos:
14
 [1]
Given Kudos: 93
Products:
My Reviews
Posts: 47
Kudos: 14
 [1]
A state has 20 cities. The train service in the state connects all cit 03 Apr 2022, 12:03
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
magic73
CrackverbalGMAT
This question can be easily solved by using the concept of Combination
The minimum number of trains needed is same as no of ways you can select 3 cities out of 20 = 20 C 3 = (20* 19* 18)/3! = (20* 19* 18)/6= 20 * 19 * 3 = 1140

Option C is the correct answer.

Thanks,
Clifin J Francis,
GMAT SME

I don't think C is correct. It should not be a combination. Consider the case with 4 cities instead of 20. 4c3 equals 4. However, you can cover 4 cities using just 3 triplets - ABC, BCD and ACD. Similarly, 6 cities can be covered in less than 6C3 (I have found a solution where 6 cities can be covered in 6 triplets).

Posted from my mobile device
Show more

ExpertsGlobal , please help here!
User avatar
ThomasK
User avatar
Joined: 21 Feb 2021
Last visit: 18 Aug 2024
Posts: 14
Own Kudos:
11
Given Kudos: 12
Posts: 14
Kudos: 11
A state has 20 cities. The train service in the state connects all cit 25 May 2022, 23:55
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Could someone please explain the underlying concept? How does the combination of 3 out of 20 ensure all stations would be covered?
avatar
scarstruck
avatar
Joined: 07 Jun 2022
Last visit: 07 Jul 2022
Posts: 1
Given Kudos: 2
Posts: 1
Kudos: 0
A state has 20 cities. The train service in the state connects all cit 21 Jun 2022, 14:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
aditijain1507
magic73
CrackverbalGMAT
This question can be easily solved by using the concept of Combination
The minimum number of trains needed is same as no of ways you can select 3 cities out of 20 = 20 C 3 = (20* 19* 18)/3! = (20* 19* 18)/6= 20 * 19 * 3 = 1140

Option C is the correct answer.

Thanks,
Clifin J Francis,
GMAT SME

I don't think C is correct. It should not be a combination. Consider the case with 4 cities instead of 20. 4c3 equals 4. However, you can cover 4 cities using just 3 triplets - ABC, BCD and ACD. Similarly, 6 cities can be covered in less than 6C3 (I have found a solution where 6 cities can be covered in 6 triplets).

Posted from my mobile device
Show more

C is correct. If you apply 4c3 for 4 cities, ABCD the answer is 4 - ABC, ABD, ACD, and BCD.
User avatar
Hoozan
User avatar
Joined: 28 Sep 2018
Last visit: 30 Dec 2025
Posts: 647
Own Kudos:
733
Given Kudos: 248
GMAT 1: 660 Q48 V33 (Online)
GMAT 2: 700 Q49 V37
Products:
My Reviews
GMAT 2: 700 Q49 V37
Posts: 647
Kudos: 733
A state has 20 cities. The train service in the state connects all cit 20 Jul 2023, 03:31
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ThomasK
Could someone please explain the underlying concept? How does the combination of 3 out of 20 ensure all stations would be covered?
Show more

ThomasK, good question. Before solving, I believe the experts should highlight their reasons to help others understand the solution set better. I am no expert, but I shall try my best.

To ensure that any set of three cities in the state is interconnected through a triplet, what is the minimum number of trains needed

The above statement hints towards using Combinations. Why? Because we need to find ALL the possible ways in which three out of the 20 cities can be connected. All the possible connections = Minimum number of trains needed (If you still do not understand why the above translates to combinations, revise the concepts of Combinations. Once you do, revisit this question)


So, the question basically says "In how many ways can you select 3 out of 20," i.e. 20C3

Answer: (C)
User avatar
EeshitaV
User avatar
Joined: 16 Jul 2023
Last visit: 24 Mar 2024
Posts: 5
Given Kudos: 34
Posts: 5
Kudos: 0
A state has 20 cities. The train service in the state connects all cit 01 Sep 2023, 00:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
magic73
CrackverbalGMAT
This question can be easily solved by using the concept of Combination
The minimum number of trains needed is same as no of ways you can select 3 cities out of 20 = 20 C 3 = (20* 19* 18)/3! = (20* 19* 18)/6= 20 * 19 * 3 = 1140

Option C is the correct answer.

Thanks,
Clifin J Francis,
GMAT SME
Show more

I don't think C is correct. It should not be a combination. Consider the case with 4 cities instead of 20. 4c3 equals 4. However, you can cover 4 cities using just 3 triplets - ABC, BCD and ACD. Similarly, 6 cities can be covered in less than 6C3 (I have found a solution where 6 cities can be covered in 6 triplets).

The fourth case is "ABD".
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 23 Apr 2026
Posts: 16,441
Own Kudos:
79,393
 [2]
Given Kudos: 484
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,441
Kudos: 79,393
 [2]
A state has 20 cities. The train service in the state connects all cit 01 Sep 2023, 02:44
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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
Show more


In the question we require selection. Out of the 20 cities, we need EVERY group of 3 cities that we can make since we want a train to connect ANY set of 3 cities.
So 20C3 will give us the number of groups of 3 cities we can make out of 20 cities.

For each such group, we will need 1 train.

Hence, 20C3 = 20*19*18/3*2*1 = 1140

Answer (C)

Check this video for an explanation of when to use combinations: https://youtu.be/tUPJhcUxllQ
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,957
Own Kudos:
1,117
Posts: 38,957
Kudos: 1,117
A state has 20 cities. The train service in the state connects all cit 23 Dec 2025, 09:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109778 posts
Krunaal
Tuck School Moderator
853 posts