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Two objects are placed on opposite corners of a cube. The [#permalink]

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15 Jan 2008, 12:35

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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?

Each object should pass trough 3 consecutive edges. Two objects can collide at the middle point of second edge in paths. There are exactly 6 middle points for a cube. Therefore, the probability is 1/6*1/6=1/36

a good question (+1) but it seems be out of GMAT.
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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?

From 2 opposite corners of a cube, there are 6 shortest routes connecting each other (along 3 edges). Out of these 6, if the same path is chosen by the 2 objects then collision will result at the center of 2 edge. So probability is 1/6.

we have 6 points. the total number of different combinations is 6(first object)*6(second object)=36 the number of combinations with collision is 6 (not 1 as I thought) Therefore, \(p = \frac{6}{36} = \frac{1}{6}\)
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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?

Ans: Each object has 6 ways to reach the other object's initial position. (passing through 3 connected edges) Hence total number of possibilities = 6 * 6 = 36

Of these 36 ways , collision will occur if each object chooses the same path, i.e both should follow one of the possible 6 ways = 6 Probability that they will collide = 6/36 = 1/6 =

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?

We need the possible short paths from the opposite corners.

The object would need to travel 2 times horizontal and once vertical to reach the opposite corner via the shortest path. Hence total number of paths = 3! (arrange HHV in diff comb).

The probability of collision can be if both the objects take the same path. Therefore = 1 / 3! = 1/6
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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?

Tell me if this is the right method too. This method that I took seemed simpler when compared.

There are 6 shortest ways to travel to the opposite corner of the cube. First object can take route in 6/6 ways.

If the second object has to collide into this, it has to choose the one route that the first object has chosen. So in 1/6 ways.

Therefore total probability = (6/6)*(1/6) = 1/6

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I used the following approach, though don't no is it right. Any object has to go 3 points to reach the opposite corner. The total number of ways is 3*2*1=6. Hence, two objects will collide if they chose the same route and the chance is 1/6.

My ans is 1/6..bt i solved in another way... there are 6 ways by which any object move from one end to its opp end(shortest way).. and if both object has to collide thn they will move on same way..means there is only one way.. so prob is 1/6

So object 1 has 3 steps to go to object 2's initial position. Object one can choose from among 3 edges, from that from two edges then with 1 edge so 3 x 2 x 1 = 6. Object 2 has the same 6 possible routes.

6 x 6 = 36 all possible comb. routes of object 1 and 2

Re: Two objects are placed on opposite corners of a cube. The [#permalink]

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25 Feb 2012, 19:10

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There are six possible paths:

The first object's path could be picked in 6 ways: 6/6 The second object's path needs to pick the same path: 1/6 Probability that they're both on the same path: 6/6 * 1/6 = 1/6 = 16.67%

Re: Two objects are placed on opposite corners of a cube. The [#permalink]

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11 Sep 2014, 03:30

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10 Mar 2016, 07:47

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Re: Two objects are placed on opposite corners of a cube. The [#permalink]

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18 Aug 2017, 21:38

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Re: Two objects are placed on opposite corners of a cube. The [#permalink]

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21 Aug 2017, 13:28

walker wrote:

1/36

Each object should pass trough 3 consecutive edges. Two objects can collide at the middle point of second edge in paths. There are exactly 6 middle points for a cube. Therefore, the probability is 1/6*1/6=1/36

a good question (+1) but it seems be out of GMAT.

I don't understand why you multiplied with 6. If you do want to consider placement of the points, then you must consider the probability of a particular placement as well, which is 1/6 for each placement. Ultimately you will end up with (1/36) x (1/6) x 6 = 1/36.

To illustrate, consider two parallel lines. If I now ask what is the probability of a collision when two objects are placed at two ends of the same line, what will be my answer? By the previous logic, it would be 2 (because there are two lines) - which is incorrect.