Mouse pellets

Question

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

Patrick_GMATFix · Answer

Moving from X to Y is equivalent to going through a series of decision points. Every time we have two options, the number of paths will double. Every time we have three options, the number of paths will triple...

The full solution below is taken from the GMATFix App.

-Patrick

Brent@GMATPrepNow · Answer

EricKryk 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

Solution:

A good 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.

The same logic can be applied to this problem. We first determine the number of ways the mouse can go from one point to the next. Notice we added in “decision points” to our diagram.

X to P1 = 1

P1 to P2 = 2

P2 to P3= 1

P3 to P4= 2

P4 to P5= 1

P5 to P6 = 3

P6 to Y = 1

Therefore, to determine the total number of ways from X to Y, we 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.

Answer:C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

GMATGuruNY · Answer

EricKryk 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

Number of ways to travel across the leftmost diamond = 2. (Either of the 2 paths.)
Number of ways to travel across the middle diamond = 2. (Either of the 2 paths.)
Number of ways to travel across the rightmost diamond = 3. (Any of the 3 paths.)
To combine these options, we multiply:
2*2*3 = 12.

The correct answer is C.

Jeff@TargetTestPrep · Answer

EricKryk 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

Solution:

A good 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.

The same logic can be applied to this problem. We first determine the number of ways the mouse can go from one point to the next. Notice we added in “decision points” to our diagram.

X to P1 = 1

P1 to P2 = 2

P2 to P3= 1

P3 to P4= 2

P4 to P5= 1

P5 to P6 = 3

P6 to Y = 1

Therefore, to determine the total number of ways from X to Y, we 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.

Answer:C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

stephanieh · Answer

GMATGuruNY wrote:EricKryk 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 Number of ways to travel across the leftmost diamond = 2. (Either of the 2 paths.) Number of ways to travel across the middle diamond = 2. (Either of the 2 paths.) Number of ways to travel across the rightmost diamond = 3. (Any of the 3 paths.) To combine these options, we multiply: 2*2*3 = 12. The correct answer is C. Awesome break down Mitch! Thank you. I don't know how you're able to make it so simple! Do you have a thought process system as you're taking in the question?

nikhilgmat31 · Answer

please attached the image.

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