It is currently 11 Dec 2017, 14:17

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
Manager
Joined: 30 Mar 2007
Posts: 177

Kudos [?]: 44 [0], given: 0

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

### Show Tags

14 Jul 2008, 05:51
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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. The 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. 20
C. 22
D. 12
E. 16

I dont even understand the question!

Kudos [?]: 44 [0], given: 0

GMAT Tutor
Joined: 24 Jun 2008
Posts: 1347

Kudos [?]: 2039 [0], given: 6

### Show Tags

14 Jul 2008, 06:35
Jamesk486 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. The 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. 20
C. 22
D. 12
E. 16

I dont even understand the question!

Game theory on the GMAT? Interesting. Where is the question from?

The question defines a game- whoever removes the last stick wins. You can remove up to 5 sticks, so if you get to a situation where there are 5 or fewer sticks left and it's your turn, you are certain to win. If you are in a situation where there are 6 sticks and it's your turn, you have to remove at least one stick, and you can't remove all 6, so your opponent certainly is left with between 1 and 5 sticks, and certainly wins. So really what you'd want to do is force your opponent into a situation where he or she has 6 sticks. You can do that if you have between 7 and 11 sticks. And you will automatically have between 7 and 11 sticks on your turn if you force your opponent to have 12 sticks- which you can do if you have between 13 and 17 sticks, and so on. As long as you can force, after your turn, the number of sticks on the table to be a multiple of 6, you can be certain to win if you play correctly. The only way Rita loses, if she goes first, is if the number of sticks on the table is a multiple of six when the game starts. That is, for the answer choices, only D) defines a situation where Rita is certain to lose (as long as Sam plays well).

Or, the longer explanation- let's look at some of the possibilities here:

If n=7, and Rita goes first, Rita will remove just 1 stick. Sam is facing 6 sticks now, so whatever he does, Sam is going to lose, Rita is going to win.

If n=12, and Rita goes first, after Rita's turn, there will be between 7 and 11 sticks left. Sam can remove enough to leave Rita with 6 sticks, so Rita is going to lose, Sam is going to win.

If n=22, and Rita goes first, Rita will remove 4 sticks. There are 18 left. No matter what Sam does, he leaves between 13 and 17 on the table. Rita can now remove enough to leave 12 sticks. After Sam moves, there are between 7 and 11- Rita removes enough to leave 6 left. etc. Sam loses, Rita wins.

And so on.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Kudos [?]: 2039 [0], given: 6

GMAT Instructor
Joined: 04 Jul 2006
Posts: 1259

Kudos [?]: 344 [0], given: 0

### Show Tags

14 Jul 2008, 08:46
As long as n is a multiple of 6, Sam can win no matter what Rita does

Kudos [?]: 344 [0], given: 0

Current Student
Joined: 28 Dec 2004
Posts: 3345

Kudos [?]: 325 [0], given: 2

Location: New York City
Schools: Wharton'11 HBS'12

### Show Tags

14 Jul 2008, 09:03
i dont get it..do they HAVE to pick up a stick on each turn?..suppose if I see 6 sticks..i am not picking any..cause i know the opponent will win..so i just keep "passing" i.e not pick up a stick..

this way there is no way anyone can win..

or maybe i am just thinking wrong???

Kudos [?]: 325 [0], given: 2

Director
Joined: 27 May 2008
Posts: 540

Kudos [?]: 370 [0], given: 0

### Show Tags

14 Jul 2008, 09:06
most probably this is a CAT questions CAT is an MBA entrance exam in India for IIMs

Kudos [?]: 370 [0], given: 0

Current Student
Joined: 04 Jan 2005
Posts: 283

Kudos [?]: 140 [0], given: 3

Location: Milan
Schools: Wharton, LBS, UChicago, Kellogg MMM (Donald Jacobs Scholarship), Stanford, HBS

### Show Tags

14 Jul 2008, 09:08
The questions reads "Each must remove 1, 2, 3, 4, or 5 sticks at a time". There is no option to remove 0 sticks.

Kudos [?]: 140 [0], given: 3

Director
Joined: 20 Sep 2006
Posts: 653

Kudos [?]: 139 [0], given: 7

### Show Tags

14 Jul 2008, 09:19
kevincan wrote:
As long as n is a multiple of 6, Sam can win no matter what Rita does

How did you get to this point that if n is multiple of 6 San will win?

Kudos [?]: 139 [0], given: 7

Current Student
Joined: 04 Jan 2005
Posts: 283

Kudos [?]: 140 [0], given: 3

Location: Milan
Schools: Wharton, LBS, UChicago, Kellogg MMM (Donald Jacobs Scholarship), Stanford, HBS

### Show Tags

14 Jul 2008, 09:47
Rao:

1. he who leaves the opponent with 6 sticks wins, as one cannot clear the table nor leave his opponent with >5 sticks. Same goes for any multiple of 6.
2. Rita starts, so it is as if John left Rita with as many sticks as there are on the table at start.
3. If those many sticks are 6 or a multiple of six, John wins.

Kudos [?]: 140 [0], given: 3

SVP
Joined: 30 Apr 2008
Posts: 1863

Kudos [?]: 627 [0], given: 32

Location: Oklahoma City
Schools: Hard Knocks

### Show Tags

14 Jul 2008, 10:00
I answer D. I think everyone else has done a great job of explaining what the question is asking for.

Jamesk486 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. The 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. 20
C. 22
D. 12
Rita goes first, if she takes 5, then 7 left, Sam takes 1, leaving 6 left, regardless of mow many Rita takes next, there is at most 5 left so Sam wins. If Rita takes only 1, then 11 left and Sam takes 5, leaving 6, Rita again, no matter what Rita does, Sam has at most 5 left and he can take them all.
E. 16

I dont even understand the question!

_________________

------------------------------------
J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a\$\$.

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 627 [0], given: 32

Director
Joined: 20 Sep 2006
Posts: 653

Kudos [?]: 139 [0], given: 7

### Show Tags

14 Jul 2008, 11:11
Rao:

1. he who leaves the opponent with 6 sticks wins, as one cannot clear the table nor leave his opponent with >5 sticks. Same goes for any multiple of 6.
2. Rita starts, so it is as if John left Rita with as many sticks as there are on the table at start.
3. If those many sticks are 6 or a multiple of six, John wins.

Thanks

Kudos [?]: 139 [0], given: 7

Re: prep question   [#permalink] 14 Jul 2008, 11:11
Display posts from previous: Sort by

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

Moderator: chetan2u

 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®.