Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 02 Jul 2015, 15:38

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
TAGS:
CEO
Joined: 15 Aug 2003
Posts: 3467
Followers: 61

Kudos [?]: 717 [0], given: 781

Rita and Sam play the following game with n sticks on a [#permalink]  09 Oct 2003, 19:38
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 2 sessions
1. 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 the value of n such that Sam can always win no matter how Rita plays?

A. 7

B. 10

C. 11

D. 12

E. 16
SVP
Joined: 03 Feb 2003
Posts: 1607
Followers: 6

Kudos [?]: 83 [0], given: 0

Rita can win if N is odd and either person takes one stick at a time. So, 7 and 11 are out. Consider 10, 12, and 16. Sam should always win.

10=5(Rita)+5(Sam)+1(Rita) Rita can win
12=5(Rita)+5(Sam)+2(Rita) Rita can win

So, 16 is left.
SVP
Joined: 30 Oct 2003
Posts: 1794
Location: NewJersey USA
Followers: 5

Kudos [?]: 43 [0], given: 0

If Sam wants to win then there should be 6 sticks left at the end and it is Rita's turn to pick. This means Sam would have picked 1-5 sticks. So Sam should have atleast one stick left prior to this trial. If atleast one stick is left then it should be so even if Rita picks up max number of sticks

so 5+1+6 = 12
Director
Joined: 28 Oct 2003
Posts: 503
Location: 55405
Followers: 1

Kudos [?]: 11 [0], given: 0

Similar topics Replies Last post
Similar
Topics:
2 The game of blackjack is played with a deck consisting of 6 27 Feb 2013, 03:54
7 Harold plays a game in which he starts with \$2. 10 04 Sep 2012, 17:18
A and B decide to play a game based on probabilities. They 3 07 Aug 2012, 06:17
28 Rita and Sam play the following game with n sticks on a 10 03 Apr 2012, 12:02
1 number of games played 4 20 Feb 2011, 08:13
Display posts from previous: Sort by