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The map above shows the trails through a wilderness area. If travel is

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The map above shows the trails through a wilderness area. If travel is  [#permalink]

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New post 21 Sep 2019, 03:18
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A
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The map above shows the trails through a wilderness area. If travel is in the direction of the arrows, how many routes along the marked trails are possible from point A to point B ?

A. 11
B. 18
C. 54
D. 108
E. 432


PS24831.01

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Re: The map above shows the trails through a wilderness area. If travel is  [#permalink]

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New post 21 Sep 2019, 04:15
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gmatt1476 wrote:
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The map above shows the trails through a wilderness area. If travel is in the direction of the arrows, how many routes along the marked trails are possible from point A to point B ?

A. 11
B. 18
C. 54
D. 108
E. 432


PS24831.01

Attachment:
2019-09-21_1417.png


From point A, 2 options and then 3 options at the start of each of the 3 loops/junctions. From the end of the last loop/junction, 1 way to reach point B

So, total number of ways = 2*3*3*3*1 = 54

IMO Option C

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Re: The map above shows the trails through a wilderness area. If travel is  [#permalink]

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New post 21 Sep 2019, 05:09
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total possible ways From A to B ; 2*3*3*3*1 ; 54
IMO C

gmatt1476 wrote:
Image
The map above shows the trails through a wilderness area. If travel is in the direction of the arrows, how many routes along the marked trails are possible from point A to point B ?

A. 11
B. 18
C. 54
D. 108
E. 432


PS24831.01

Attachment:
2019-09-21_1417.png
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Re: The map above shows the trails through a wilderness area. If travel is  [#permalink]

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New post 31 Oct 2019, 11:29
= (3*3*3) +(3*3*3)=54
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Re: The map above shows the trails through a wilderness area. If travel is  [#permalink]

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New post 31 Oct 2019, 17:05
A to B, going through top path 1*3*3*3*1 = 27
A to B, going through bottom path 1*3*3*3*1 = 27
Total path = 27 + 27 = 54
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Re: The map above shows the trails through a wilderness area. If travel is  [#permalink]

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New post 03 Nov 2019, 20:44
1
gmatt1476 wrote:
Image
The map above shows the trails through a wilderness area. If travel is in the direction of the arrows, how many routes along the marked trails are possible from point A to point B ?

A. 11
B. 18
C. 54
D. 108
E. 432


PS24831.01

Attachment:
2019-09-21_1417.png


We see that the diagram has a horizontal line symmetry (if we draw a horizontal line through A and B). Therefore, if we find the number of routes from A to B in the upper half of the diagram, we can just multiply that by 2 to obtain the total number of routes from A to B in the entire diagram.

In the upper half of the diagram, counting each point starting from A and ending at B, we have 1, 3, 3, 3 and 1 routes between each pair of consecutive points, therefore, the number of routes is 1 x 3 x 3 x 3 x 1 = 27. Multiplying this by 2, we have a total of 54 routes from A to B.

Answer: C
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Re: The map above shows the trails through a wilderness area. If travel is  [#permalink]

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New post 04 Nov 2019, 06:56
gmatt1476 wrote:
Image
The map above shows the trails through a wilderness area. If travel is in the direction of the arrows, how many routes along the marked trails are possible from point A to point B ?

A. 11
B. 18
C. 54
D. 108
E. 432


PS24831.01

Attachment:
2019-09-21_1417.png



Total Routes = 2*[3*3*3] = 54

ANSWER: C
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Re: The map above shows the trails through a wilderness area. If travel is  [#permalink]

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New post 07 Dec 2019, 17:10
Hi All,

We're told that the map above shows the trails through a wilderness area and travel must be done in the direction of the arrows. We're asked for the total number of routes along the marked trails that are possible from point A to point B. This is a variation on a Permutation question and requires just a bit of Multiplication to solve.

At the first 'step' on the trail, we have 2 options (go "up" or go "down"). After making that choices, we then have 3 additional 'steps' (with 3 options at each step) before we take the final path to point B. Thus, the total number of possible routes is:

(2)(3)(3)(3) = 54 different routes

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Re: The map above shows the trails through a wilderness area. If travel is  [#permalink]

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New post 03 Jan 2020, 16:08
MBA HOUSE KEY CONCEPT: combinatorics multiplication principle


A to B upper line (5 steps) = 1 x 3 x 3 x 3 x 1 = 27

or (or means +)

A to B bottom line (5 steps) = 1 x 3 x 3 x 3 x 1 = 27

27 + 27 = 54

C :tongue_opt1
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Re: The map above shows the trails through a wilderness area. If travel is   [#permalink] 03 Jan 2020, 16:08
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