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.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

256 teams play in a state soccer tournament. A team is elimi [#permalink]
28 Apr 2013, 06:07

1

This post received KUDOS

1

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

73% (01:58) correct
27% (01:21) wrong based on 96 sessions

256 teams play in a state soccer tournament. A team is eliminated from the tournament after one loss. In the first round, all 256 teams play one game. If a team wins, it advances to the next round, where it plays another winning team. This process repeats itself until only one team is left, having advanced through each round without losing. How many games are played in the tournament?

Re: 256 teams play in a state soccer tournament. A team is elimi [#permalink]
28 Apr 2013, 06:33

7

This post received KUDOS

In order to one team to win, all other teams should lose. So we can calculate the number of games as the number of team-losers. There are 255 such teams. The answer should be A.

P.S. If course you can calculate as sum of 128 games in first round, 64 in second, 32 in third, 16 in fourth, 8 in fifth, 4 in sixth, 2 in seventh, and 1 in eights. Still you get the same answer A. But not so fast. _________________

I'm happy, if I make math for you slightly clearer And yes, I like kudos:)

Re: 256 teams play in a state soccer tournament. A team is elimi [#permalink]
28 Apr 2013, 06:35

Hi my friends, this is my solution to this problem in round 1, there's 2^8 teams with 2^7 games are played. and then in round 2, there's 2^7 teams left wiht 2^6 games are played in the last round, there's 2 teams left with 1 game are played so the games that is played is A=2^7+2^6+...+2+1 we must find the value of A we have 2.A=2^8+2^7+...^2^2+2 and then 2.A-A=(2^8+2^7+...+2^2+2)-(2^7+2^6+...+2+1)=2^8-1 so we have A=2^8-1=255 The answer is A My friends, I think if you want to solve this problem fast, you should know that 256=2^8 _________________

Life is not easy I knew that and now I don't even expect life to be easy

Last edited by retailingvnsupernova on 28 Apr 2013, 06:36, edited 1 time in total.

Re: 256 teams play in a state soccer tournament. A team is elimi [#permalink]
28 Apr 2013, 06:42

2

This post received KUDOS

The most beautiful thing in this problem that you don't need to do any calculations. The answer will be always the number if teams-1. _________________

I'm happy, if I make math for you slightly clearer And yes, I like kudos:)

Re: 256 teams play in a state soccer tournament. A team is elimi [#permalink]
28 Apr 2013, 06:49

smyarga wrote:

The most beautiful thing in this problem that you don't need to do any calculations. The answer will be always the number if teams-1.

Yes, after solving this problem as I posted above, I think that if you have 2^n teams, there's will always be 2^n-1 games played smyarga, please explain to me more clearly why there's 255 losers so we will have 255 games played. I think your solution is much faster and more clever than mine. _________________

Life is not easy I knew that and now I don't even expect life to be easy

Re: 256 teams play in a state soccer tournament. A team is elimi [#permalink]
28 Apr 2013, 07:01

1

This post received KUDOS

retailingvnsupernova wrote:

smyarga wrote:

The most beautiful thing in this problem that you don't need to do any calculations. The answer will be always the number if teams-1.

Yes, after solving this problem as I posted above, I think that if you have 2^n teams, there's will always be 2^n-1 games played smyarga, please explain to me more clearly why there's 255 losers so we will have 255 games played. I think your solution is much faster and more clever than mine.

With pleasure. Every game has exactly one loser. To calculate the number of games is the same as calculate the number of losers. Every team except the winner loses only one game. So the number of games is the number of teams except the winner. Hope this helps. _________________

I'm happy, if I make math for you slightly clearer And yes, I like kudos:)

Re: 256 teams play in a state soccer tournament. A team is elimi [#permalink]
28 Apr 2013, 07:08

smyarga wrote:

Every game has exactly one loser. To calculate the number of games is the same as calculate the number of losers. Every team except the winner loses only one game. So the number of games is the number of teams except the winner. Hope this helps.

oh my god, my brain is too lazy Thank you ^^ _________________

Life is not easy I knew that and now I don't even expect life to be easy

Re: 256 teams play in a state soccer tournament. A team is elimi [#permalink]
28 Apr 2013, 10:05

smyarga wrote:

In order to one team to win, all other teams should lose. So we can calculate the number of games as the number of team-losers. There are 255 such teams. The answer should be A.

P.S. If course you can calculate as sum of 128 games in first round, 64 in second, 32 in third, 16 in fourth, 8 in fifth, 4 in sixth, 2 in seventh, and 1 in eights. Still you get the same answer A. But not so fast.

i was over thinking this problem, thanks for explaining a quick and easy method.. _________________

Consider giving +1 Kudo when my post helps you. Also, Good Questions deserve Kudos..!

Re: 256 teams play in a state soccer tournament. A team is elimi [#permalink]
07 May 2013, 23:30

We have simple set of geometrical progression with first element 128 (128 pairs = 256). We have 8 rounds to final game, so A number of games (formula of sum for n elements of geometrical progression ) = (128* (q^8-1))/0,5-1 = (128*(1-0,0625)(1+0,0625))/0,5 = First Impression that answer is 256, but you should look for slightly different answer such as 255 Where q- step of geometrical progression = 0,5!

Re: 256 teams play in a state soccer tournament. A team is elimi [#permalink]
16 Jun 2014, 01:33

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. _________________