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

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

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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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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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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.

The correct answer is (1).

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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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Jeffrey Miller Head of GMAT Instruction

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