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The diagram above shows the various paths along which
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24 Aug 2020, 10:12
24 Aug 2020, 10:12
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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
Re: The diagram above shows the various paths along which
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24 Aug 2020, 10:12
24 Aug 2020, 10:12
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Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
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Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
For more theory and practice see our GRE - Math Book
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Re: The diagram above shows the various paths along which
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24 Aug 2020, 10:15
24 Aug 2020, 10:15
1
Carcass wrote:
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)
Answer: C
Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.
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