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# Amy has to visit towns B and C in any order. The roads conne

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Amy has to visit towns B and C in any order. The roads conne  [#permalink]

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Updated on: 05 Jan 2014, 05:52
1
9
00:00

Difficulty:

65% (hard)

Question Stats:

56% (01:54) correct 44% (01:54) wrong based on 189 sessions

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Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?

A. 10
B. 8
C. 6
D. 4
E. 2

Source: Other - http://www.majortests.com/gmat/problem_solving_test01

Originally posted by kumar83 on 04 Jan 2014, 23:47.
Last edited by Bunuel on 05 Jan 2014, 05:52, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Amy has to visit towns B and C in any order. The roads conne  [#permalink]

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18 Jun 2014, 21:27
6
3
kumar83 wrote:
Attachment:
1.gif

Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?

A. 10
B. 8
C. 6
D. 4
E. 2

Source: Other - http://www.majortests.com/gmat/problem_solving_test01

From A, there are two things Amy can do - go to B or to C. Since the paths are not symmetrical along B and C, you will need to consider them separately.

Case 1: Go to B first
A to B - 1 way
B to C - 2 ways
C to A - 2 ways

Total number of ways in this case = 1*2*2 = 4

Case 2: Go to C first
A to C - 2 ways
C to B - 2 ways
B to A - 1 way

Total number of ways in this case = 2*2*1 = 4

Total number of ways = 4+4 = 8
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Karishma
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Re: Ques. Amy has to visit towns B and C in any order.  [#permalink]

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05 Jan 2014, 00:23
kumar83 wrote:
Source: Other - http://www.majortests.com/gmat/problem_solving_test01

Attachment:
1.gif

Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?
A. 10
B. 8
C. 6
D. 4
E. 2

Clockwise:
Lets assume Weight of A is 1, So the weight of B is 1 as only one route is there to reach.
Weight of C = 1+1 (2 ways to reach C from B) = 2
Weight of A (the last point in the journey ) = 2 + 2 (2 ways to reach A from C) = 4

Similarly for Anti-clokwise :
Lets assume weight of A is 1, so the weight of C = 1+1 (2 ways to reach to C from A) = 2
Weight of B = 2+2 (as there are 2 ways to reach B from C) = 4
Weight to reach A = 4 (as only one way to reach A from C) = 4

hence total is 4+4 = 8 ways (option B))

For any questions on route, this is the best way to solve.
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Re: Ques. Amy has to visit towns B and C in any order.  [#permalink]

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05 Jan 2014, 00:32
To make the concept a little more clear, I have just added a example which is attach.

How many ways a person can reach from A to I if only direction allowed to traverse is from left to right?

Weight of A = 1
Weight of B = 1
weight of C = 1
Weight of D = 1
weight of E = 1+1 = 2
weight of F =1
weight of G = 1
weight of H = 1+ 2 + 1 = 4
weight of I = 1 + 4 + 1 = 6

so 6 ways are possible.

The questions can be made a little more complex as there might be a circular path to a node or in one of the path back traversal is allowed (only once for example), then the weights can be calculated again. This method takes care of double counting and with practice, it can be done in secs.
One of my Quant teacher used to say "Clicking the option takes more time than to solve the question".
Attachments

File comment: Sample problem in Routes

RouteMapSampleProblems.png [ 16.6 KiB | Viewed 24218 times ]

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Re: Amy has to visit towns B and C in any order. The roads conne  [#permalink]

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18 Jun 2014, 19:54
Hi Bunuel,

Can you shed some light on this concept of weights? Is this type of question frequent in gmat?
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Re: Amy has to visit towns B and C in any order. The roads conne  [#permalink]

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19 Jun 2014, 02:03
3
Refer diagram below:

Possible combinations via route A - B - C - A = 4

a - b1 - c1

a - b1 - c2

a - b2 - c1

a - b2 - c2

Possible combinations via route A - C - B - A = 4

Total = 8

Attachments

1.gif [ 2.18 KiB | Viewed 22428 times ]

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Re: Amy has to visit towns B and C in any order. The roads conne  [#permalink]

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19 Jun 2014, 06:26
1
Thanks Paresh and Karishma .Kudos to u both
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Re: Amy has to visit towns B and C in any order. The roads conne  [#permalink]

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05 Nov 2014, 02:02
Thanks Karishma for a simple explanation. +1 to you!
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Re: Amy has to visit towns B and C in any order. The roads conne  [#permalink]

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12 Aug 2018, 17:54
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Re: Amy has to visit towns B and C in any order. The roads conne   [#permalink] 12 Aug 2018, 17:54
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