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The map above shows the trails through a wilderness area. If travel is : Problem Solving (PS)
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Re: The map above shows the trails through a wilderness area. If travel is [#permalink]
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total possible ways From A to B ; 2*3*3*3*1 ; 54
IMO C

gmatt1476 wrote:

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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= (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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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]
gmatt1476 wrote:

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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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

Final Answer:

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Re: The map above shows the trails through a wilderness area. If travel is [#permalink]
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]
Number of routes from point A to B.

Given:
There are 2 routes from A to B.
There are 3 Nodes and each nodes have 3 possible routes to reach from one node to other.

So possible routes are 2*3*3*3 = 54

Ans: C
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Re: The map above shows the trails through a wilderness area. If travel is [#permalink]
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gmatt1476 wrote:

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


HI Experts GMATGuruNY, MentorTutoring, generis,

I'm bit confused here. Why is it not \(2*(3^2)*(3^2)*(3^2)\) ?
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Re: The map above shows the trails through a wilderness area. If travel is [#permalink]
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NandishSS wrote:
gmatt1476 wrote:

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

HI Experts GMATGuruNY, MentorTutoring, generis,

I'm bit confused here. Why is it not \(2*(3^2)*(3^2)*(3^2)\) ?

Hello, NandishSS. The reason you cannot square each junction with three choices is that there is a linear pathway once you start up or down from Point A. What you are saying is that there are two choices, then nine, nine, and nine, whereas you can see quite clearly that once you choose an upper or lower track, there will be three, three, and three choices, with one way to get to Point B at the end. Hence, there are 2 * (3 * 3 * 3) * 1 ways to get from Point A to Point B. Choice (D) is a nice trap answer, but once the upper or lower pathway has been selected, there is a single way to get to the endpoint.

I hope that helps. Thank you for tagging me.

- Andrew
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Re: The map above shows the trails through a wilderness area. If travel is [#permalink]
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NandishSS wrote:
gmatt1476 wrote:

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


HI Experts GMATGuruNY, MentorTutoring, generis,

I'm bit confused here. Why is it not \(2*(3^2)*(3^2)*(3^2)\) ?


Hi NandishSS,

When dealing with certain types of Permutation or Combination questions, it can sometimes help to "put yourself in the story" so that you can logically work through the steps involved in the calculation.

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.

At the first 'step' on the trail, we have 2 options (go "up" or go "down"). After you make that choice....
we then have 3 options ("up" path, "middle" path or "down" path). After you make that choice...
we then have another 3 options ("up" path, "middle" path or "down" path). After you make that choice...
we then have one more set of 3 options ("up" path, "middle" path or "down" path). After you make that choice, you are at the end of the path (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]
Why can't we do 2*3*3*3*2?
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Re: The map above shows the trails through a wilderness area. If travel is [#permalink]
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tittoo wrote:
Why can't we do 2*3*3*3*2?

Hello, tittoo. The reason we cannot multiply by 2 at the end is that that would indicate a choice of paths at the end when in fact just a single path exists once the upper or lower track has been selected at Point A. It might help to tease apart the two tracks and think of the number of choices at each step independently:

Upper track from Point A: 1 (to get on the upper track)-3-3-3-1 (to get to Point B) → 1 * 3 * 3 * 3 * 1 = 27 options

Lower track from Point A: 1-3-3-3-1 → 1 * 3 * 3 * 3 * 1 = 27 options

27 + 27 = 54

Sometimes it can pay to take a little more time to understand the problem rather than look for a shortcut, particularly when the GMAT™ is known for its trickery. I hope that explanation helps. Good luck with your studies.

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Re: The map above shows the trails through a wilderness area. If travel is [#permalink]
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gmatt1476 wrote:

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


To not get confused,

Upper half of the diagram,

Mark the meeting points with some letters
A-L-M-N-O-B

A-L = 1 way
L-M = 3 way
M-N = 3 way
N-O = 3 way
O-B = 1 way

So upper half can be done in (1*3*3*3*1)=27 ways

Similarly, for lower half, 27 ways

Total 54 ways
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The map above shows the trails through a wilderness area. If travel is [#permalink]
Expert Reply
gmatt1476 wrote:

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


Answer: Option C

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The map above shows the trails through a wilderness area. If travel is [#permalink]
gmatt1476 wrote:

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

Applying the combinations technique to this problem:

1. Selecting \(1\) out of the \(2\) available paths at A \(=\) \(2C1\) \(=\) \(2\)
2. Once we select a path, we come across 3 sets of splits with 3 paths within each
3. At the first split we need to choose \(1\) out of \(3 = 3C1 = 3\)
4. At the second split we need to choose \(1\) out of \(3 = 3C1 = 3\)
5. At the third split we need to choose \(1\) out of \(3 = 3C1 = 3\)
6. Then, there are is only \(1\) available path \(= 1C1 = 1\)

Putting together the above points \(= 2 * 3 * 3 * 3 * 1 = 54\)

Ans. C
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Re: The map above shows the trails through a wilderness area. If travel is [#permalink]
There are two paths:

Each path has 3 * 3 * 3 = 27 different routes from point A to point B

To account for the two paths: 27 * 2 = 54

Answer is C.
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Re: The map above shows the trails through a wilderness area. If travel is [#permalink]
Hi,
Starting from point A, I have 2 choices of route AND then I have 3 choices AND 3 choices AND 3 choices. Last tray doesn't count as I have no other choice than taking it.

2*3*3*3= 2*27=54

Answer C)
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