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# A certain basketball team that has played 2/3 of its games

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A certain basketball team that has played 2/3 of its games [#permalink]  05 Jun 2008, 00:50
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A certain basketball team that has played 2/3 of its games has a record of 17 wins and 3 losses. What is the greatest number of the remaining games that the team can lose and still win at least 3/4 of all of its games?
(A) 7
(B) 6
(C) 5
(D) 4
(E) 3
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Re: How to solve this problem [#permalink]  05 Jun 2008, 00:56
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D

Since it's played 2/3 of its games and played a total of 20 games so far, it has 10 games left.
To win 3/4 of all games (30 games) the number of games that the team can lose is 30/4, which is 7.25 = 7 games
The team has already lost 3 games, so at most it can lose only 4 more if it wants to win 3/4 of all games.
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Re: How to solve this problem [#permalink]  05 Jun 2008, 01:31

i agree with the reasoning given by Seb

whts the OA for this
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Re: How to solve this problem [#permalink]  05 Jun 2008, 05:35
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nitika22 wrote:
A certain basketball team that has played 2/3 of its games has a record of 17 wins and 3 losses. What is the greatest number of the remaining games that the team can lose and still win at least 3/4 of all of its games?
(A) 7
(B) 6
(C) 5
(D) 4
(E) 3

So it needs to play 20 =2/3x --> 10 more games (total of 30 games).

w/30=3/4 --> 4w=90 --> w=45/2? 22.5=w.

Thus it needs to win at least 22.5-17 = 5.5 or 6. 20+6= 26 wins.

Thus it can only loose 4 more games. A total of 7.

This problem took slightly longer than 2min b/c the decimals, which I think make this problem "difficult", caught me off guard.
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Re: How to solve this problem [#permalink]  05 Jun 2008, 18:16
I solved it till 17/30... but since I got a decimal number got confused...
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Re: How to solve this problem [#permalink]  05 Jun 2008, 22:21
The team has alredy played 17+3=20 games.
These are 2/3rd of total games. thus, total games are 3/2 *20=30.No of games yet to be played are30-20=10.
The team has to win total of 3/4 games i.e. 3/4*30=90/4=22.5 say 23 games. Its has already won 17 games. so remaining games to be won are 23-17=6.
Now question asks how many games it can lose. i.e. 10-6=4
D should be the OA.
nitika22 wrote:
A certain basketball team that has played 2/3 of its games has a record of 17 wins and 3 losses. What is the greatest number of the remaining games that the team can lose and still win at least 3/4 of all of its games?
(A) 7
(B) 6
(C) 5
(D) 4
(E) 3
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Re: How to solve this problem [#permalink]  05 Jun 2008, 22:28
nitika22 wrote:
A certain basketball team that has played 2/3 of its games has a record of 17 wins and 3 losses. What is the greatest number of the remaining games that the team can lose and still win at least 3/4 of all of its games?
(A) 7
(B) 6
(C) 5
(D) 4
(E) 3

D,

23-17= 6 wins needed; 4 can be lost out of 10.
Re: How to solve this problem   [#permalink] 05 Jun 2008, 22:28
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