Author 
Message 
TAGS:

Hide Tags

Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1211
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs

A certain board game has a row of squares numbered 1 to 100.
[#permalink]
Show Tags
29 Feb 2012, 11:58
Question Stats:
48% (01:16) correct 52% (01:43) wrong based on 122 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
"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."
My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/myirlogbookdiary133264.html
GMAT Club Premium Membership  big benefits and savings



Math Expert
Joined: 02 Sep 2009
Posts: 50036

Re: A certain board game has a row of squares numbered 1 to 100.
[#permalink]
Show Tags
29 Feb 2012, 12:12



Manager
Joined: 22 Feb 2012
Posts: 86
GMAT 1: 740 Q49 V42 GMAT 2: 670 Q42 V40
GPA: 3.47
WE: Corporate Finance (Aerospace and Defense)

Re: A certain board game has a row of squares numbered 1 to 100.
[#permalink]
Show Tags
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 600700 level...



Math Expert
Joined: 02 Sep 2009
Posts: 50036

Re: A certain board game has a row of squares numbered 1 to 100.
[#permalink]
Show Tags
29 Feb 2012, 12:18



Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1211
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs

Re: A certain board game has a row of squares numbered 1 to 100.
[#permalink]
Show Tags
01 Mar 2012, 07:04
Bunuel, I have a doubt: The piece must end in the range 4256, 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 4256. 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."
My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/myirlogbookdiary133264.html
GMAT Club Premium Membership  big benefits and savings



Math Expert
Joined: 02 Sep 2009
Posts: 50036

Re: A certain board game has a row of squares numbered 1 to 100.
[#permalink]
Show Tags
01 Mar 2012, 07:08
metallicafan wrote: Bunuel, I have a doubt: The piece must end in the range 4256, 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 4256.
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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1211
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs

Re: A certain board game has a row of squares numbered 1 to 100.
[#permalink]
Show Tags
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? Thank you for your time!
_________________
"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."
My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/myirlogbookdiary133264.html
GMAT Club Premium Membership  big benefits and savings



Intern
Joined: 17 May 2012
Posts: 1

Re: A certain board game has a row of squares numbered 1 to 100.
[#permalink]
Show Tags
07 Jan 2013, 11:18
There are three sections of interest in this problem 1) locations (4248) 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 (5056) 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



Manager
Joined: 18 Oct 2011
Posts: 87
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01302013
GPA: 3.3

Re: A certain board game has a row of squares numbered 1 to 100.
[#permalink]
Show Tags
07 Jan 2013, 11:44
7 spaces from 49 to the right > 56 7 spaces from 49 to the left > 42
5642 = 14 +1 = 15
therefore 15/100 = 15% (D)



Intern
Joined: 27 Dec 2012
Posts: 13

Re: A certain board game has a row of squares numbered 1 to 100.
[#permalink]
Show Tags
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 (6338) Posted from GMAT ToolKit



Math Expert
Joined: 02 Sep 2009
Posts: 50036

Re: A certain board game has a row of squares numbered 1 to 100.
[#permalink]
Show Tags
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 (6338) Posted from GMAT ToolKitFirst 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 4256, inclusive), thus the probability is 15/100. Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 27 Dec 2012
Posts: 13

Re: A certain board game has a row of squares numbered 1 to 100.
[#permalink]
Show Tags
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. 4256). 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? Posted from GMAT ToolKit



Math Expert
Joined: 02 Sep 2009
Posts: 50036

Re: A certain board game has a row of squares numbered 1 to 100.
[#permalink]
Show Tags
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. 4256). 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? Posted from GMAT ToolKitYes, we should simply consider the range from 42 to 56, inclusive.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



NonHuman User
Joined: 09 Sep 2013
Posts: 8515

Re: A certain board game has a row of squares numbered 1 to 100.
[#permalink]
Show Tags
26 Sep 2018, 06:23
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: A certain board game has a row of squares numbered 1 to 100. &nbs
[#permalink]
26 Sep 2018, 06:23






