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# The diagram above shows the various paths along which a mous

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The diagram above shows the various paths along which a mous [#permalink]

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17 Dec 2012, 07:31
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The diagram above shows the various paths along which a mouse can travel from point X, where it is released, to point Y, where it is rewarded with a food pellet. How many different paths from X to Y can the mouse take if it goes directly from X to Y without retracing any point along a path?

(A) 6
(B) 7
(C) 12
(D) 14
(E) 17
[Reveal] Spoiler: OA

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Re: The diagram above shows the various paths along which a mous [#permalink]

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17 Dec 2012, 07:33
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The diagram above shows the various paths along which a mouse can travel from point X, where it is released, to point Y, where it is rewarded with a food pellet. How many different paths from X to Y can the mouse take if it goes directly from X to Y without retracing any point along a path?

(A) 6
(B) 7
(C) 12
(D) 14
(E) 17

There are 3 forks along the path: 2 choices for the first one, 2 for the second and 3 for the third. Hence total # of ways is 2*2*3=12.

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Re: The diagram above shows the various paths along which a mous [#permalink]

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17 Dec 2012, 07:56
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Also counting is fast

12 or 11 paths. 12 is the only among the options.

So C
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Re: The diagram above shows the various paths along which a mous [#permalink]

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17 Dec 2012, 11:26
Bunuel wrote:
Attachment:
Path.png
The diagram above shows the various paths along which a mouse can travel from point X, where it is released, to point Y, where it is rewarded with a food pellet. How many different paths from X to Y can the mouse take if it goes directly from X to Y without retracing any point along a path?

(A) 6
(B) 7
(C) 12
(D) 14
(E) 17

There are 3 forks along the path: 2 choices for the first one, 2 for the second and 3 for the third. Hence total # of ways is 2*2*3=12.

Dear Bunnel,
Could you please clarify it more...How the forks are working?

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Re: The diagram above shows the various paths along which a mous [#permalink]

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17 Dec 2012, 11:46
Drik wrote:
Bunuel wrote:
Attachment:
Path.png
The diagram above shows the various paths along which a mouse can travel from point X, where it is released, to point Y, where it is rewarded with a food pellet. How many different paths from X to Y can the mouse take if it goes directly from X to Y without retracing any point along a path?

(A) 6
(B) 7
(C) 12
(D) 14
(E) 17

There are 3 forks along the path: 2 choices for the first one, 2 for the second and 3 for the third. Hence total # of ways is 2*2*3=12.

Dear Bunnel,
Could you please clarify it more...How the forks are working?

is pretty simple: one the first fork you have 2 choices - right and left; idem for the second one; 3 for the third one: right, left and central to the goal. 2*2*3=12

That's it
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Re: The diagram above shows the various paths along which a mous [#permalink]

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28 Dec 2012, 01:52
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Attachment:
Path.png
The diagram above shows the various paths along which a mouse can travel from point X, where it is released, to point Y, where it is rewarded with a food pellet. How many different paths from X to Y can the mouse take if it goes directly from X to Y without retracing any point along a path?

(A) 6
(B) 7
(C) 12
(D) 14
(E) 17

Technique here is to multiply the number of choices in every point of decision:
$$2*2*3 = 12$$

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Re: The diagram above shows the various paths along which a mous [#permalink]

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10 Sep 2013, 23:24
Hi Brunel - Would you help us with more such questions?

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Re: The diagram above shows the various paths along which a mous [#permalink]

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11 Sep 2013, 01:43
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Re: The diagram above shows the various paths along which a mous [#permalink]

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15 Jul 2014, 02:49
Why is it multiplied here ? Why can't we add all options ?

Posted from my mobile device

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Re: The diagram above shows the various paths along which a mous [#permalink]

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15 Jul 2014, 03:03
kshitij89 wrote:
Why is it multiplied here ? Why can't we add all options ?

Posted from my mobile device

Because of Principle of Multiplication: if one event can occur in m ways and a second can occur independently of the first in n ways, then the two events can occur in m*n ways.

For example, if you have two pairs of shoes, A and B, and two shirts, X and Y, then there will be 2*2 = 4 shoes-shirt combinations:
AX;
AY;
BX;
BY.

Hope it's clear.
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Re: The diagram above shows the various paths along which a mous [#permalink]

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21 Oct 2015, 15:16
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Re: The diagram above shows the various paths along which a mous [#permalink]

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21 Jun 2016, 10:24
Attachment:
Path.png
The diagram above shows the various paths along which a mouse can travel from point X, where it is released, to point Y, where it is rewarded with a food pellet. How many different paths from X to Y can the mouse take if it goes directly from X to Y without retracing any point along a path?

(A) 6
(B) 7
(C) 12
(D) 14
(E) 17

The best way to solve this problem is to use the idea of the fundamental counting principle. In a more standard form you could be asked a question, such as if Tom as 3 belts, 4 ties, and 6 shirts, how many outfits could he make with those items? We can consider each item a decision point, i.e., belts, ties, and shirts. To solve this, we just need to multiply the number of decisions Tom can make together, so:

3 x 4 x 6 = 72 ways.

Tom has 72 options when dressing with those items.

This same logic can be applied to this problem here. We can first determine the number ways the mouse can go from one point to the next.

X to A = 1

A to B = 2

B to C = 1

C to D= 2

D to E = 1

E to F = 3

F to Y =1

Therefore, to find the total number of ways from X to Y we can multiply all these numbers together:

1 x 2 x 1 x 2 x 1 x 3 x 1 = 12 ways.

There are 12 different paths.

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Re: The diagram above shows the various paths along which a mous [#permalink]

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17 Sep 2016, 07:42

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Re: The diagram above shows the various paths along which a mous [#permalink]

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14 Oct 2016, 03:43
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TheLordCommander wrote:

For the first point you have two options (2C1) for the C, same for the second point (2C1), for third point you have 3 options (3C1).

--> 2C1 * 2C1 * 3C1 = 2*2*3 = 12

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Re: The diagram above shows the various paths along which a mous [#permalink]

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14 May 2017, 23:07
We will do addition here also to answer the question posted earlier.
a We will first add 2 choice[1+1]
b Then we will add 2 choices [1+1]
c Then we will add 3 choices [1+1+1]
Then we will multiply the straight lines first to get 1
Then we will multiply the different probabilities a,b,c to get 12

Attachment:
Path.png
The diagram above shows the various paths along which a mouse can travel from point X, where it is released, to point Y, where it is rewarded with a food pellet. How many different paths from X to Y can the mouse take if it goes directly from X to Y without retracing any point along a path?

(A) 6
(B) 7
(C) 12
(D) 14
(E) 17

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Re: The diagram above shows the various paths along which a mous [#permalink]

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28 Aug 2017, 15:38
Top Contributor
Attachment:
Path.png
The diagram above shows the various paths along which a mouse can travel from point X, where it is released, to point Y, where it is rewarded with a food pellet. How many different paths from X to Y can the mouse take if it goes directly from X to Y without retracing any point along a path?

(A) 6
(B) 7
(C) 12
(D) 14
(E) 17

First recognize that, in order to get from point X to point Y, we MUST travel through points A,B,C,D,E and F.

So, we can take the task of getting from point X to Y and break it into stages.

Stage 1: Move from point X to point A
There's only 1 possible route, so we can complete stage 1 in 1 way.

Stage 2: Move from point A to point B
There are 2 possible routes, so we can complete stage 2 in 2 ways.

Stage 3: Move from point B to point C
There's only 1 possible route, so we can complete stage 3 in 1 way.

Stage 4: Move from point C to point D
There are 2 possible routes, so we can complete stage 4 in 2 ways.

Stage 5: Move from point D to point E
There's only 1 possible route, so we can complete stage 5 in 1 way.

Stage 6: Move from point E to point F
There are 3 possible routes, so we can complete stage 6 in 3 ways.

Stage 7: Move from point F to point Y
There's only 1 possible route, so we can complete stage 7 in 1 way.

By the Fundamental Counting Principle (FCP), we can complete all 7 stages (and thus move from point X to point Y) in (1)(2)(1)(2)(1)(3)(1) ways (= 12 ways)

[Reveal] Spoiler:
C

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

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Re: The diagram above shows the various paths along which a mous   [#permalink] 28 Aug 2017, 15:38
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