equipped with a power device

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Sat Feb 21, 2009 4:36 am

Two objects are placed on opposite corners of a cube. The objects are designed only to move along the edges of the cube and are equipped with a power device which allows them to do so at the same constant speed of S inches per minute. If both objects begin moving at the same time, each taking one of the shortest paths towards the initial position of the other, what is the probability that the two objects will collide?

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Source: Beat The GMAT — Problem Solving | Sat Feb 21, 2009 4:36 am

dendude: Master | Next Rank: 500 Posts; Posts: 160; Joined: Fri May 30, 2008 7:10 pm; Thanked: 10 times; GMAT Score:600

by dendude » Sat Feb 21, 2009 8:33 am

My guess is 1/36

Each object has 6 possible paths of traversal to the opposite corner i.e 2 along each of the 3 sides
Hence the probability that both take the same route is 1/36

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ven4gmat: Junior | Next Rank: 30 Posts; Posts: 29; Joined: Sun Feb 08, 2009 11:29 am; Thanked: 3 times

by ven4gmat » Sat Feb 21, 2009 8:35 am

In order to go from one corner to the opposite corner along the sides there will be 6 routes. Hence the two objects can chooses their paths in 6x6=36 different ways. In order to collide, both of them should take the same path.

So probability = 1/36

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sureshbala: Master | Next Rank: 500 Posts; Posts: 319; Joined: Wed Feb 04, 2009 10:32 amFollowed by: 9 members; Location: Delhi; Thanked: 84 times

by sureshbala » Sat Feb 21, 2009 8:36 am

Yes, i will got with 1/36. Explanation is already provided by our friends..

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bmlaud: Master | Next Rank: 500 Posts; Posts: 174; Joined: Thu Jan 08, 2009 12:04 am; Thanked: 5 times; GMAT Score:620

by bmlaud » Sat Feb 21, 2009 11:01 am

The movement is a three segment move, the first move from one corner can be in 3 ways, the second one in two ways.

Total ways 3*2*1 = 6 ways

same for the other object too so the probability of collision is 1/(6*6)=1/36

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