Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

52% (01:49) correct
47% (00:49) wrong based on 36 sessions

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?

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

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.

Re: A certain board game has a row of squares numbered 1 to 100. [#permalink]
29 Feb 2012, 11:18

Expert's post

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.
_________________

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

"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

Re: A certain board game has a row of squares numbered 1 to 100. [#permalink]
01 Mar 2012, 06:08

Expert's post

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!

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

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.

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

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

Expert's post

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?