On a railway route between two places A and B, there are 10

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mensanumber: Senior | Next Rank: 100 Posts; Posts: 31; Joined: Wed Oct 23, 2013 6:43 amFollowed by: 1 member; Thanked: 2 times; GMAT Score:750

by mensanumber » Wed Mar 07, 2018 5:54 am

On a railway route between two places A and B, there are 10 stations on the way. If 4 new stations are to be added, how many types of new tickets will be required if each ticket is issued for a one-way journey?

1) 108
2) 14
3) 48
4) 96

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regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Wed Mar 07, 2018 7:27 am

There are 10+2 = 12 stops along the line before the 4 new stops

Each of the 4 new stations then can go back and forth between these 12 stops, so 4x12x2 = 96 new one way tickets

Each of the 4 stations can go back and forth between each other. How many ways to select 2 stations from 4 = 4!/2! = 12

Total new one way tickets = 96 + 12 = 108, 1

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Mar 07, 2018 11:18 am

mensanumber wrote:On a railway route between two places A and B, there are 10 stations on the way. If 4 new stations are to be added, how many types of new tickets will be required if each ticket is issued for a one-way journey?

1) 108
2) 14
3) 48
4) 96

Current number of ticket options:
There are currently 12 stops: A, B, and the 10 stops between them.
Number of options for the departure stop = 12.
Number of options for the arrival stop = 11.
To combine these options, we multiply:
12*11 = 132.

New number of ticket options:
After 4 stops are added, the total number of stops will increase from 12 to 16.
Number of options for the departure stop = 16.
Number of options for the arrival stop = 15.
To combine these options, we multiply:
16*15 = 240.

New types of tickets:
(new number of ticket options) - (current number of ticket options) = 240 - 132 = 108.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Mon Mar 12, 2018 10:32 am

mensanumber wrote:On a railway route between two places A and B, there are 10 stations on the way. If 4 new stations are to be added, how many types of new tickets will be required if each ticket is issued for a one-way journey?

1) 108
2) 14
3) 48
4) 96

With 10 stations between A and B, the current route has 10 + 2 = 12 stations. Thus the current number of tickets for a one-way journey between two stations is 12P2 = 12 x 11 = 132. With the 4 new stations added, the number of tickets for a one-way journey between two stations will be 16P2 = 16 x 15 = 240 = (14 x 13)/2. Thus, the number of new tickets needed to be issued is 240 - 132 = 108.

Answer: A

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