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A certain board game has a row of squares numbered 1 to 100.

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A certain board game has a row of squares numbered 1 to 100. [#permalink] New post 29 Feb 2012, 10:58
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Question Stats:

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A certain board game has a row of squares numbered 1 to 100. If a game piece is placed on a random square and then moved 7 consecutive spaces in a random direction, what is the probability the piece ends no more than 7 spaces from the square numbered 49?

(A) 7%
(B) 8%
(C) 14%
(D) 15%
(E) 28%

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[Reveal] Spoiler: OA

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Re: A certain board game has a row of squares numbered 1 to 100. [#permalink] New post 29 Feb 2012, 11:12
Expert's post
metallicafan wrote:
A certain board game has a row of squares numbered 1 to 100. If a game piece is placed on a random square and then moved 7 consecutive spaces in a random direction, what is the probability the piece ends no more than 7 spaces from the square numbered 49?

(A) 7%
(B) 8%
(C) 14%
(D) 15%
(E) 28%

Enjoy!

Source: http://www.gmathacks.com


No more than 7 spaces from 49 means in the range from 49-7=42 to 49+7=56, inclusive. Total numbers in this range 56-42+1=15, the probability favorable/total=15/100=0.15.

Answer: D.

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Re: A certain board game has a row of squares numbered 1 to 100. [#permalink] New post 29 Feb 2012, 11:15
Quote:
If a game piece is placed on a random square and then moved 7 consecutive spaces in a random direction


Bunuel - thanks for the response - is the quote above just to distract you from the solution or was it needed?

I read this and thought it was much more complex than 600-700 level...
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Re: A certain board game has a row of squares numbered 1 to 100. [#permalink] New post 29 Feb 2012, 11:18
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AbeinOhio wrote:
Quote:
If a game piece is placed on a random square and then moved 7 consecutive spaces in a random direction


Bunuel - thanks for the response - is the quote above just to distract you from the solution or was it needed?

I read this and thought it was much more complex than 600-700 level...


Yes, "a game piece is placed on a random square and then moved 7 consecutive spaces in a random direction" just means that a game piece is placed on a random square.

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Re: A certain board game has a row of squares numbered 1 to 100. [#permalink] New post 01 Mar 2012, 06:04
Bunuel, I have a doubt:
The piece must end in the range 42-56, right? Also, the question says that the game piece is placed on a random square and then moved 7 consecutive spaces in a random direction.

So, if we wanted that the piece be placed in square #42, for instance, there are two possible squares in which the piece could be originally placed: 35 and 49. If it is placed in #35 we have to move the piece to the right, and if it is placed in #49, we have to move the piece to the left. So, there are two possibilities to obtain the desired result. This happens with every square in the range 42-56.

However, if we wanted that the piece be placed in square #1, there are not two possibilities. The only square in which the piece can be originally placed is #8 (then we move it 7 squares to the left).

Based on this reasoning, the probability could not be \frac{15}{100} because there are numbers that have more succesful outcomes than others as I have shown.

I think that I am overanalyzing the problem, but I cannot solve that doubt. Thanks!

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Re: A certain board game has a row of squares numbered 1 to 100. [#permalink] New post 01 Mar 2012, 06:08
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metallicafan wrote:
Bunuel, I have a doubt:
The piece must end in the range 42-56, right? Also, the question says that the game piece is placed on a random square and then moved 7 consecutive spaces in a random direction.

So, if we wanted that the piece be placed in square #42, for instance, there are two possible squares in which the piece could be originally placed: 35 and 49. If it is placed in #35 we have to move the piece to the right, and if it is placed in #49, we have to move the piece to the left. So, there are two possibilities to obtain the desired result. This happens with every square in the range 42-56.

However, if we wanted that the piece be placed in square #1, there are not two possibilities. The only square in which the piece can be originally placed is #8 (then we move it 7 squares to the left).

Based on this reasoning, the probability could not be \frac{15}{100} because there are numbers that have more succesful outcomes than others as I have shown.

I think that I am overanalyzing the problem, but I cannot solve that doubt. Thanks!


Yes, you are overthinking it.

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Re: A certain board game has a row of squares numbered 1 to 100. [#permalink] New post 01 Mar 2012, 06:19
Bunuel wrote:
Yes, you are overthinking it.


Thank you. But could you provide more detail why my reasoning is wrong?
Thank you for your time! :-D

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Re: A certain board game has a row of squares numbered 1 to 100. [#permalink] New post 07 Jan 2013, 10:18
There are three sections of interest in this problem
1) locations (42-48) and user has to move the piece to it's right -> probability P1 -> (7/100) * (1/2)
2) location 49 is selected (User can move it any direction and is still in the limit) -> probability P2 -> 1/100
3) locations (50-56) and user has to move the piece to it's left -> probability P3 -> (7/100) *(1/2)

So total probability is (P1+P2+P3) -> 8/100 i.e 8%

Let me know your thoughts
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Re: A certain board game has a row of squares numbered 1 to 100. [#permalink] New post 07 Jan 2013, 10:44
7 spaces from 49 to the right ---> 56
7 spaces from 49 to the left ----> 42

56-42 = 14 +1 = 15

therefore 15/100 = 15% (D)
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Re: A certain board game has a row of squares numbered 1 to 100. [#permalink] New post 23 May 2013, 08:18
I am getting 28 as my answer... Can somebody explain why are we ignoring extended ranges?

Explanation - I can select 35, move right, end up in 42 (49- 7) or else select 63, move left, end up in 56 (49+7). So why not 28 (63-38)

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Re: A certain board game has a row of squares numbered 1 to 100. [#permalink] New post 23 May 2013, 08:55
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Asishp wrote:
I am getting 28 as my answer... Can somebody explain why are we ignoring extended ranges?

Explanation - I can select 35, move right, end up in 42 (49- 7) or else select 63, move left, end up in 56 (49+7). So why not 28 (63-38)

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First of all you should include 35 and 63. So, the range is 30 (from 28 to 62, inclusive). Next, sine the game piece is moved in a random direction, then in half of the case it will move in the wrong direction (away from the range 42-56, inclusive), thus the probability is 15/100.

Hope it's clear.

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Re: A certain board game has a row of squares numbered 1 to 100. [#permalink] New post 23 May 2013, 09:25
Ok ... May be I am not getting it yet and Confusing extra numbers 35, 30, 28, 62 above ..

However if I concentrate on last part of sentence and if I understand it correct, it means that there are two ways I can fall at a number (left or right). But from either way there are equal chances of falling into the range and also equal chances of going out of the range (i.e. 42-56). Since these chances cancel each other out, it is not required to consider the direction to reach a number.. Just the range of number maters .. Am I right?

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Re: A certain board game has a row of squares numbered 1 to 100. [#permalink] New post 23 May 2013, 09:29
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Asishp wrote:
Ok ... May be I am not getting it yet and Confusing extra numbers 35, 30, 28, 62 above ..

However if I concentrate on last part of sentence and if I understand it correct, it means that there are two ways I can fall at a number (left or right). But from either way there are equal chances of falling into the range and also equal chances of going out of the range (i.e. 42-56). Since these chances cancel each other out, it is not required to consider the direction to reach a number.. Just the range of number maters .. Am I right?

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Yes, we should simply consider the range from 42 to 56, inclusive.

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Re: A certain board game has a row of squares numbered 1 to 100.   [#permalink] 23 May 2013, 09:29
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