It is currently 17 Nov 2017, 13:02

Close

GMAT Club Daily Prep

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Rita and Sam play the following game with n sticks on a

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

2 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 31 Oct 2011
Posts: 338

Kudos [?]: 1252 [2], given: 18

Rita and Sam play the following game with n sticks on a [#permalink]

Show Tags

New post 03 Apr 2012, 13:02
2
This post received
KUDOS
18
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

37% (02:06) correct 63% (01:42) wrong based on 534 sessions

HideShow timer Statistics

Rita and Sam play the following game with n sticks on a table. Each must remove 1,2,3,4, or 5 sticks at a time on alternate turns, and no stick that is removed is put back on the table. Tha one who removes the last stick (or sticks) from the table wins. If Rita goes first, which of the following is a value of n such that Sam can always win no matter how Rita plays?

A. 7
B. 10
C. 11
D. 12
E. 16
[Reveal] Spoiler: OA

Kudos [?]: 1252 [2], given: 18

Expert Post
10 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132507 [10], given: 12323

Re: Rita and Sam play the following game with n sticks on a [#permalink]

Show Tags

New post 03 Apr 2012, 13:21
10
This post received
KUDOS
Expert's post
6
This post was
BOOKMARKED
eybrj2 wrote:
Rita and Sam play the following game with n sticks on a table. Each must remove 1,2,3,4, or 5 sticks at a time on alternate turns, and no stick that is removed is put back on the table. Tha one who removes the last stick (or sticks) from the table wins. If Rita goes first, which of the following is a value of n such that Sam can always win no matter how Rita plays?

A. 7
B. 10
C. 11
D. 12
E. 16


If the number of sticks on a table is a multiple of 6, then the second player will win in any case (well if the player is smart enough).

Consider n=6, no matter how many sticks will be removed by the first player (1, 2, 3 ,4 or 5), the rest (5, 4, 3, 2, or 1) can be removed by the second one.

The same for n=12: no matter how many sticks will be removed by the first player 1, 2, 3 ,4 or 5, the second one can remove 5, 4, 3, 2, or 1 so that to leave 6 sticks on the table and we are back to the case we discussed above.

Answer: D.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132507 [10], given: 12323

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132507 [0], given: 12323

Re: Rita and Sam play the following game with n sticks on a [#permalink]

Show Tags

New post 31 May 2013, 06:22

Kudos [?]: 132507 [0], given: 12323

Manager
Manager
avatar
Joined: 14 Nov 2011
Posts: 144

Kudos [?]: 21 [0], given: 103

Location: United States
Concentration: General Management, Entrepreneurship
GPA: 3.61
WE: Consulting (Manufacturing)
GMAT ToolKit User
Re: Rita and Sam play the following game with n sticks on a [#permalink]

Show Tags

New post 03 Jun 2013, 21:57
Bunuel wrote:
eybrj2 wrote:
Rita and Sam play the following game with n sticks on a table. Each must remove 1,2,3,4, or 5 sticks at a time on alternate turns, and no stick that is removed is put back on the table. Tha one who removes the last stick (or sticks) from the table wins. If Rita goes first, which of the following is a value of n such that Sam can always win no matter how Rita plays?

A. 7
B. 10
C. 11
D. 12
E. 16


If the number of sticks on a table is a multiple of 6, then the second player will win in any case (well if the player is smart enough).

Consider n=6, no matter how many sticks will be removed by the first player (1, 2, 3 ,4 or 5), the rest (5, 4, 3, 2, or 1) can be removed by the second one.

The same for n=12: no matter how many sticks will be removed by the first player 1, 2, 3 ,4 or 5, the second one can remove 5, 4, 3, 2, or 1 so that to leave 6 sticks on the table and we are back to the case we discussed above.

Answer: D.



Hi Bunnel,
Please explain this:

N = 12, here 1 and 2 shows steps in a game: rita picks 5 first, out of remaining 7 sam can pick a maximum of 5, which leaves 2 sticks after round one. On her next chance rita can pick 2 and win.

R S
1 5 5
2 2 > Rita wins

similarly:
R S
1 4 5
2 3 > Rita wins
R S
1 2 5
2 5 > Rita wins
R S
1 2 2
2 5 3 > Sam wins
R S
1 2 3
2 5 2 > Sam wins

So both can win when n=12.
I agree for n=6, but not for n=12.

Kudos [?]: 21 [0], given: 103

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132507 [1], given: 12323

Re: Rita and Sam play the following game with n sticks on a [#permalink]

Show Tags

New post 04 Jun 2013, 03:46
1
This post received
KUDOS
Expert's post
cumulonimbus wrote:
Bunuel wrote:
eybrj2 wrote:
Rita and Sam play the following game with n sticks on a table. Each must remove 1,2,3,4, or 5 sticks at a time on alternate turns, and no stick that is removed is put back on the table. Tha one who removes the last stick (or sticks) from the table wins. If Rita goes first, which of the following is a value of n such that Sam can always win no matter how Rita plays?

A. 7
B. 10
C. 11
D. 12
E. 16


If the number of sticks on a table is a multiple of 6, then the second player will win in any case (well if the player is smart enough).

Consider n=6, no matter how many sticks will be removed by the first player (1, 2, 3 ,4 or 5), the rest (5, 4, 3, 2, or 1) can be removed by the second one.

The same for n=12: no matter how many sticks will be removed by the first player 1, 2, 3 ,4 or 5, the second one can remove 5, 4, 3, 2, or 1 so that to leave 6 sticks on the table and we are back to the case we discussed above.

Answer: D.



Hi Bunnel,
Please explain this:

N = 12, here 1 and 2 shows steps in a game: rita picks 5 first, out of remaining 7 sam can pick a maximum of 5, which leaves 2 sticks after round one. On her next chance rita can pick 2 and win.

R S
1 5 5
2 2 > Rita wins

similarly:
R S
1 4 5
2 3 > Rita wins
R S
1 2 5
2 5 > Rita wins
R S
1 2 2
2 5 3 > Sam wins
R S
1 2 3
2 5 2 > Sam wins

So both can win when n=12.
I agree for n=6, but not for n=12.


That;s not correct.

Both players can win BUT if the number of sticks on a table is a multiple of 6, then the second player will win in any case IF the player is smart enough.

n=12: no matter how many sticks will be removed by the first player 1, 2, 3 , 4 or 5, the second one can remove 5, 4, 3, 2, or 1, RESPECTIVELY so that to leave 6 sticks on the table.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132507 [1], given: 12323

Manager
Manager
avatar
Joined: 14 Nov 2011
Posts: 144

Kudos [?]: 21 [0], given: 103

Location: United States
Concentration: General Management, Entrepreneurship
GPA: 3.61
WE: Consulting (Manufacturing)
GMAT ToolKit User
Re: Rita and Sam play the following game with n sticks on a [#permalink]

Show Tags

New post 04 Jun 2013, 19:12
If the number of sticks on a table is a multiple of 6, then the second player will win in any case (well if the player is smart enough).

Consider n=6, no matter how many sticks will be removed by the first player (1, 2, 3 ,4 or 5), the rest (5, 4, 3, 2, or 1) can be removed by the second one.

The same for n=12: no matter how many sticks will be removed by the first player 1, 2, 3 ,4 or 5, the second one can remove 5, 4, 3, 2, or 1 so that to leave 6 sticks on the table and we are back to the case we discussed above.

Answer: D.[/quote]


Hi Bunnel,
Please explain this:

N = 12, here 1 and 2 shows steps in a game: rita picks 5 first, out of remaining 7 sam can pick a maximum of 5, which leaves 2 sticks after round one. On her next chance rita can pick 2 and win.

R S
1 5 5
2 2 > Rita wins

similarly:
R S
1 4 5
2 3 > Rita wins
R S
1 2 5
2 5 > Rita wins
R S
1 2 2
2 5 3 > Sam wins
R S
1 2 3
2 5 2 > Sam wins

So both can win when n=12.
I agree for n=6, but not for n=12.[/quote]

That;s not correct.

Both players can win BUT if the number of sticks on a table is a multiple of 6, then the second player will win in any case IF the player is smart enough.

n=12: no matter how many sticks will be removed by the first player 1, 2, 3 , 4 or 5, the second one can remove 5, 4, 3, 2, or 1, RESPECTIVELY so that to leave 6 sticks on the table.[/quote]

got it. thanks.
is this gmat question ?

Kudos [?]: 21 [0], given: 103

Expert Post
12 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7736

Kudos [?]: 17766 [12], given: 235

Location: Pune, India
Re: Rita and Sam play the following game with n sticks on a [#permalink]

Show Tags

New post 04 Jun 2013, 21:26
12
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
eybrj2 wrote:
Rita and Sam play the following game with n sticks on a table. Each must remove 1,2,3,4, or 5 sticks at a time on alternate turns, and no stick that is removed is put back on the table. Tha one who removes the last stick (or sticks) from the table wins. If Rita goes first, which of the following is a value of n such that Sam can always win no matter how Rita plays?

A. 7
B. 10
C. 11
D. 12
E. 16


I would like to point out one thing about these questions based on games. These games are made to have a sure shot winner (if both players play intelligently and to win) under certain conditions. If A and B are playing, B's move will be decided by A's move if B has to win i.e. there are complementary moves. For example, in this question, if A picks 2 sticks, B must pick 4 sticks. If A picks 3 sticks, B must pick 3 too. So to solve these questions you need to find this particular complementary relation.

This question tell us that one can pick 1/2/3/4/5 sticks. This means n must be greater than 5 to have a game else the one who picks first will pick all and win. If n = 6, the first one to pick must pick at least 1 and at most 5 sticks leaving anywhere between 5 to 1 sticks for the other player. The other player will definitely win. If n= 7, the first player will pick 1 and leave the other player with 6 sticks. The first player will win. So the object of the game is to leave 6 sticks for your opponent. If the number of sticks is a multiple of 6, you can always make a complementary move to your opponent's move and ensure that you leave your opponent with 6 sticks. For example, if your opponent picks 1 stick, you pick 5, if he picks 2 sticks, you pick 4 and so on.

So when Rita starts, Sam can complement her move each time and leave her with 6 sticks at the end if the total number of sticks is a multiple of 6. There is only one multiple of 6 in the options.
Hence, answer must be (D)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17766 [12], given: 235

Manager
Manager
avatar
Joined: 07 Apr 2012
Posts: 124

Kudos [?]: 13 [0], given: 45

Location: United States
Concentration: Entrepreneurship, Operations
Schools: ISB '15
GMAT 1: 590 Q48 V23
GPA: 3.9
WE: Operations (Manufacturing)
Re: Rita and Sam play the following game with n sticks on a [#permalink]

Show Tags

New post 02 Sep 2013, 21:05
so what is the generalisation in such questions or we just have to analyze everytime?

Kudos [?]: 13 [0], given: 45

Expert Post
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7736

Kudos [?]: 17766 [0], given: 235

Location: Pune, India
Re: Rita and Sam play the following game with n sticks on a [#permalink]

Show Tags

New post 02 Sep 2013, 21:28
ygdrasil24 wrote:
so what is the generalisation in such questions or we just have to analyze everytime?


To have a sure shot winner, you need complimentary moves. You have to analyze to figure out the complimentary move every time, of course.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17766 [0], given: 235

Expert Post
Director
Director
User avatar
B
Joined: 17 Dec 2012
Posts: 623

Kudos [?]: 534 [0], given: 16

Location: India
Re: Rita and Sam play the following game with n sticks on a [#permalink]

Show Tags

New post 02 Sep 2013, 21:39
ygdrasil24 wrote:
so what is the generalisation in such questions or we just have to analyze everytime?


The trick is to rephrase the question in more general terms. In this case it would be: What is the number that can always be divided into even number of times when each division can be up to 5. The answer is one greater than 5 which is 6 because whatever be the first value chosen, the second value can be chosen such that 6 can always be divided into two. The same idea can be extended to the multiples of 6 such that they can always be divided even number of times given that each division can be from 1 to 5.
_________________

Srinivasan Vaidyaraman
Sravna
http://www.sravnatestprep.com/regularcourse.php

Premium Material
Standardized Approaches

Kudos [?]: 534 [0], given: 16

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15703

Kudos [?]: 281 [0], given: 0

Premium Member
Re: Rita and Sam play the following game with n sticks on a [#permalink]

Show Tags

New post 25 Nov 2016, 07:46
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

Kudos [?]: 281 [0], given: 0

Re: Rita and Sam play the following game with n sticks on a   [#permalink] 25 Nov 2016, 07:46
Display posts from previous: Sort by

Rita and Sam play the following game with n sticks on a

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.