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# Two points A and B are connected to each other via three paths,.......

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3078
Two points A and B are connected to each other via three paths,.......  [#permalink]

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21 Nov 2018, 05:03
00:00

Difficulty:

15% (low)

Question Stats:

83% (01:12) correct 17% (01:31) wrong based on 84 sessions

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Two points A and B are connected to each other via three paths, as shown in the figure. A person needs to make a round trip from A to B and then back to A, using any of the three paths. What is the ratio of the possible total distances covered, if he never uses the same path for both onward and return journey?

A. 20: 24: 30
B. 20: 25: 27
C. 22: 24: 27
D. 22: 25: 30
E. 22: 25: 27

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Concentration: Operations, General Management
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Re: Two points A and B are connected to each other via three paths,.......  [#permalink]

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21 Nov 2018, 06:42
1
For every path from A to B we have two path to return ( As same path cannot be used)

Case-1
Path from A to B 12 miles
Coming back either using 10 miles or 15 miles
So distance covered can be either 22 or 27 miles

Case-2
Path from A to B 10 miles
Coming back either using 12 miles or 15 miles
So distance covered can be either 22 or 25 miles

Case-3
Path from A to B 15 miles
Coming back either using 10 miles or 12 miles
So distance covered can be either 25 or 27 miles

In any case ratio of total distance covered will be 22:25:27
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Joined: 04 Jan 2015
Posts: 3078
Re: Two points A and B are connected to each other via three paths,.......  [#permalink]

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23 Nov 2018, 07:16
1

Solution

Given:
• There are three paths between A and B
• A person needs to take a round trip between A and B
• He can use any of the three paths, but he will use different paths for onward and return journeys

To find:
• The ratio of all the possible distances that he covers

Approach and Working:
• Distance covered in path, I + II = 12 + 10 = 22 miles
• Distance covered in path, II + III = 10 + 15 = 25 miles
• Distance covered in path, I + III = 12 + 15 = 27 miles

Therefore, ratio of possible distances covered = 22: 25: 27

Hence the correct answer is Option E.

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Re: Two points A and B are connected to each other via three paths,.......   [#permalink] 23 Nov 2018, 07:16
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