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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]

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29 Feb 2012, 11:58
00:00

Difficulty:

55% (hard)

Question Stats:

51% (01:59) correct 49% (01:25) wrong based on 65 sessions

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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%

Enjoy!

Source: http://www.gmathacks.com
[Reveal] Spoiler: OA

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Re: A certain board game has a row of squares numbered 1 to 100. [#permalink]

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29 Feb 2012, 12:12
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.

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Re: A certain board game has a row of squares numbered 1 to 100. [#permalink]

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29 Feb 2012, 12:15
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]

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29 Feb 2012, 12:18
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]

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01 Mar 2012, 07:04
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]

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01 Mar 2012, 07:08
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]

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01 Mar 2012, 07:19
Bunuel wrote:
Yes, you are overthinking it.

Thank you. But could you provide more detail why my reasoning is wrong?
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Re: A certain board game has a row of squares numbered 1 to 100. [#permalink]

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07 Jan 2013, 11:18
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%

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Re: A certain board game has a row of squares numbered 1 to 100. [#permalink]

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07 Jan 2013, 11:44
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]

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23 May 2013, 09:18
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]

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23 May 2013, 09:55
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)

Posted from GMAT ToolKit

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]

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23 May 2013, 10:25
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]

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23 May 2013, 10:29
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, 10:29
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