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Mouse pellets

This topic has 4 expert replies and 2 member replies
EricKryk Senior | Next Rank: 100 Posts Default Avatar
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Mouse pellets

Post Thu Feb 20, 2014 8:32 am

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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stephanieh Newbie | Next Rank: 10 Posts Default Avatar
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Post Mon Jun 29, 2015 9:58 pm
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?

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nikhilgmat31 Legendary Member Default Avatar
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518 messages
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10
Test Date:
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Top Reply
Post Thu Jul 02, 2015 10:50 pm
please attached the image.

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stephanieh Newbie | Next Rank: 10 Posts Default Avatar
Joined
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Posted:
7 messages
Upvotes:
1
Post Mon Jun 29, 2015 9:58 pm
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?

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nikhilgmat31 Legendary Member Default Avatar
Joined
12 May 2015
Posted:
518 messages
Upvotes:
10
Test Date:
3 Oct
Target GMAT Score:
750
Post Thu Jul 02, 2015 10:50 pm
please attached the image.

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Post Mon Jun 29, 2015 6:59 am
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:

ttp://postimg.org/image/6ynwb3eqr/" target="_blank">

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

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Post Thu Feb 20, 2014 12:33 pm
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.

_________________
Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.

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Thanked by: stephanieh
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