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

Question

https://gmatclub.com/forum/download/file.php?id=50452 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 2019-09-21_1417.png

ScottTargetTestPrep · Accepted Answer

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

CareerGeek · Answer

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

Pls Hit kudos if you like the solution

Posted from my mobile device

Archit3110 · Answer

total possible ways From A to B ; 2*3*3*3*1 ; 54
IMO C

saukrit · Answer

= (3*3*3) +(3*3*3)=54

AKASHSURANA · Answer

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

dabaobao · Answer

Total Routes = 2*  = 54

ANSWER: C

EMPOWERgmatRichC · Answer

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:  C

GMAT assassins aren't born, they're made, 
Rich

Mbahousegmat · Answer

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

akadiyan · Answer

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

NandishSS · Answer

HI Experts  GMATGuruNY ,  MentorTutoring ,  generis ,

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

AndrewN · Answer

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

EMPOWERgmatRichC · Answer

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

GMAT assassins aren't born, they're made, 
Rich

tittoo · Answer

Why can't we do 2*3*3*3*2?

AndrewN · Answer

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.

- Andrew

ProfChaos · Answer

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

GMATinsight · Answer

Answer: Option C

GMATinsight's Solution

https://www.youtube.com/watch?v=AIsIT99x5cQ

https://gmatinsight.com/all-courses/

Pritishd · Answer

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

Basshead · Answer

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.

Sabby · Answer

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)

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards