Walkabout 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
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. So, be sure to learn it.
RELATED VIDEOS
_________________
Brent Hanneson – Creator of gmatprepnow.com
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
Many students fail to maximize their quant score NOT because they lack the skills to solve certain questions but because they don’t understand what the GMAT is truly testing -
Learn more