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The figure shows the paths from point A to point E in a video game. Ho

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The figure shows the paths from point A to point E in a video game. Ho  [#permalink]

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New post 01 Apr 2018, 10:42
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

65% (01:25) correct 35% (02:02) wrong based on 74 sessions

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The figure shows the paths from point A to point E in a video game. How many different ways can a player move from point A to point E and then back from point E to point A without retracing a previous path taken?

(A) 300
(B) 7,200
(C) 14,400
(D) 28,800
(E) 57,600


Attachment:
2018-04-01_2140.png
2018-04-01_2140.png [ 28.84 KiB | Viewed 695 times ]

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Re: The figure shows the paths from point A to point E in a video game. Ho  [#permalink]

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New post 01 Apr 2018, 10:55
Bunuel wrote:
Image

The figure shows the paths from point A to point E in a video game. How many different ways can a player move from point A to point E and then back from point E to point A without retracing a previous path taken?

(A) 300
(B) 7,200
(C) 14,400
(D) 28,800
(E) 57,600


Attachment:
2018-04-01_2140.png


Total number of path to go from A-E=4*2*6*5
From E to A with diff path=4-1*2-1*6-1*5-1=3*1*5*4

So total path =4*2*6*5*3*1*5*4=14,400
Option C
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Re: The figure shows the paths from point A to point E in a video game. Ho  [#permalink]

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New post 01 Apr 2018, 10:57
1
Bunuel wrote:

The figure shows the paths from point A to point E in a video game. How many different ways can a player move from point A to point E and then back from point E to point A without retracing a previous path taken?

(A) 300
(B) 7,200
(C) 14,400
(D) 28,800
(E) 57,600




Instead of solving our problem in one go, we'll split it into smaller, simpler problems.
This is a Logical approach.

There are a total of
4 ways from A to B
2 from B to C
6 from C to D
5 from D to E

So, going from A to E we have a total of 4*2*6*5 = 240 options.
On the way back, we have to remove the routes we've already used, so we have
5 - 1 = 4 from E to D
6 - 1 = 5 from D to C
2 - 1 = 1 from C to B
4 - 1 = 3 from B to A
This gives 4*5*1*3 = 60 options.

In total we have 240*60 - 14,400 possible combinations.

(C) is our answer.
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Re: The figure shows the paths from point A to point E in a video game. Ho   [#permalink] 01 Apr 2018, 10:57
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