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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]

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27 Jan 2007, 11:25
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55% (hard)

Question Stats:

58% (01:13) correct 42% (01:32) wrong based on 368 sessions

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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: A certain basketball team that has played 2/3 of its games  [#permalink]

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31 Dec 2011, 10:16
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sgoll wrote:
Q. 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

Thanks

Total x
2/3x = 20
X= 30
total = 30
Played 20
remaining = 10

total win = 3/4 of total = 22.5 or 23
total losses = 30 - 23 = 7 games
so max losses from the remaining 10 games = 7 - 3 = 4
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Re: A certain basketball team that has played 2/3 of its games  [#permalink]

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07 Jul 2014, 22:22
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sgoll 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

17 wins, 3 losses - total 20 games played.
The team has played 2/3rd of all games so total number of games = 30

3/4th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games. It has already lost 3 games so it can lose another 4 at most.

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Re: A certain basketball team that has played 2/3 of its games  [#permalink]

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08 Jul 2014, 02:42
Win .......... Lose ............. Total

17 .............. 3 ..................... 20

$$\frac{2}{3} rd = 20$$; so total matches to be played $$= 20 * \frac{3}{2} = 30$$

Assume "x" as matches lost in the following 10 games

27 - x ............ x + 3 ..................... 30

25% of the matches (Max) can be lost

$$\frac{x+3}{30} = \frac{25}{100}$$

$$x = \frac{30}{4} - 3$$

$$x = \frac{18}{4} = 4$$ (Ignore decimal)

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Re: A certain basketball team that has played 2/3 of its games  [#permalink]

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07 Mar 2016, 19:41
sgoll 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

is it really a 700 lvl question? solved it in 1 minute...
if 17+3 games =2/3 of total, then they have to play 10 more games.
total 30 games.
3/4 of 30 is 22.5 - since we are talking about games, we need to round up - 23 games need to win.
so from 10 left, 6 has to win, and 4 might lose. 4 is the greatest number of games the team can lose.
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Re: A certain basketball team that has played 2/3 of its games  [#permalink]

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10 Aug 2017, 10:37
sgoll 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

Since 20 games (17 wins and 3 losses) represent 2/3 of the total games played, we can say:

(2/3)(total) = 20

Total = 30

Thus, there are 10 games left.

We need to determine how many games can be lost so that at least 3/4 of the games are won, or in other words, so that at most 1/4 of the games are lost. We can let x = the number of games that can be lost and we have:

(x + 3)/30 ≤ 1/4

4x + 12 ≤ 30

4x ≤ 18

x ≤ 4.5

X must be an integer, and the largest integer less than or equal to 4.5 is 4.

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Re: A certain basketball team that has played 2/3 of its games  [#permalink]

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20 Sep 2017, 15:40
Top Contributor
sgoll 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

Given:
The team has played 2/3 of its games. The team has played 20 games.
If 2/3 of the total number of games = 20, then the total number of games = 30.
This means that there are 10 games remaining.

We want the team to win at least 3/4 of its games.
3/4 of 30 = 22.5
So, in order to win at least 3/4 of the games, the team must win a total of 23 games or more.

The team has already won 17 games, so it needs to win at least 6 of the remaining 10 games.
Or we can say that the team can lose 4 games at most.

Cheers,
Brent
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Re: A certain basketball team that has played 2/3 of its games &nbs [#permalink] 20 Sep 2017, 15:40
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