GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
In a game where there are 10 cards on the table, the player who remove
[#permalink]
29 Mar 2022, 02:00
29 Mar 2022, 02:00
Expert Reply
00:00
Question Stats:
70% (01:56) correct
30% (02:05) wrong based on 10 sessions
Hide Show timer Statistics
In a game where there are 10 cards on the table, the player who removes the last card wins. Three players in the order of A, B, and C remove at least 1 but no more than 5 cards at a turn. If Player C removes only 1 at her turn, how many cards must player A remove on her first turn in order to make sure that she wins the game?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Part of the project: Skill Builder Project for a Q170
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
Retired Moderator
Joined: 09 Nov 2021
Status:GRE Tutor London and Online
Affiliations: Private GMAT/GRE Tutor London
Posts: 76
Given Kudos: 6
Re: In a game where there are 10 cards on the table, the player who remove
[#permalink]
29 Mar 2022, 04:47
29 Mar 2022, 04:47
1
This is a maximize-minimize question:
We are told that Player C removes only 1 card. Fundamentally, we need to understand what the options are for each player. Remember, each player must remove at least one card. Assuming no rational errors (that is, A mistakenly takes fewer than necessary to win), then the winning situation would be guaranteed if A takes 3 cards at the beginning.
Here's why:
If A gets greedy and removes 5 cards, then B can remove 4 and C takes 1, winning.
If A removes 4 cards, then B can remove 5 cards, but C will then win. This is what we don't want.
--However, if B removes 4 cards and C takes 1, then A can win.
--If B removes 3 cards and C takes 1, then A can win.
--If B removes 2 cards and C takes 1, then A can win.
--If B removes 1 card and C takes 1, then A can win.
However, if A removes 3 cards or fewer, we get a situation like the following:
--A removes 3 cards, then B removes 5 cards, C removes 1. A can win.
--A removes 3 cards, then B removes 4 cards, C removes 1. A can win.
--A removes 3 cards, then B removes 3 cards, C removes 1. A can win.
--A removes 3 cards, then B removes 2 cards, C removes 1. A can win.
Again, assuming no logical errors on A's part, selecting 4 cards leaves the possibility that C can win, but selecting 3 cards leaves the window open for A.
The answer is C, 3 cards.
We are told that Player C removes only 1 card. Fundamentally, we need to understand what the options are for each player. Remember, each player must remove at least one card. Assuming no rational errors (that is, A mistakenly takes fewer than necessary to win), then the winning situation would be guaranteed if A takes 3 cards at the beginning.
Here's why:
If A gets greedy and removes 5 cards, then B can remove 4 and C takes 1, winning.
If A removes 4 cards, then B can remove 5 cards, but C will then win. This is what we don't want.
--However, if B removes 4 cards and C takes 1, then A can win.
--If B removes 3 cards and C takes 1, then A can win.
--If B removes 2 cards and C takes 1, then A can win.
--If B removes 1 card and C takes 1, then A can win.
However, if A removes 3 cards or fewer, we get a situation like the following:
--A removes 3 cards, then B removes 5 cards, C removes 1. A can win.
--A removes 3 cards, then B removes 4 cards, C removes 1. A can win.
--A removes 3 cards, then B removes 3 cards, C removes 1. A can win.
--A removes 3 cards, then B removes 2 cards, C removes 1. A can win.
Again, assuming no logical errors on A's part, selecting 4 cards leaves the possibility that C can win, but selecting 3 cards leaves the window open for A.
The answer is C, 3 cards.
gmatclubot
Re: In a game where there are 10 cards on the table, the player who remove [#permalink]
29 Mar 2022, 04:47
Moderators:
