The diagram above shows the various paths along which a mouse can travel from point X, where it is released, to point Y,

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Fri May 28, 2021 1:34 pm

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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

OA C

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)

Answer: C

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch this video: https://www.gmatprepnow.com/module/gmat- ... /video/775

You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat ... /video/776

Then you can try solving the following questions:

EASY
- https://www.beatthegmat.com/what-should- ... 67256.html
- https://www.beatthegmat.com/counting-pro ... 44302.html
- https://www.beatthegmat.com/picking-a-5- ... 73110.html
- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html


MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
- https://www.beatthegmat.com/arabian-hors ... 50703.html
- https://www.beatthegmat.com/sub-sets-pro ... 73337.html
- https://www.beatthegmat.com/combinatoric ... 73180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-sep ... 71047.html
- https://www.beatthegmat.com/combinatoric ... 67079.html


DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
- https://www.beatthegmat.com/permutation- ... 73915.html
- https://www.beatthegmat.com/permutation-t122873.html
- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/combinations-t123249.html


Cheers,
Brent