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
The OA is D.
This PS question is hard to me. How can I establish the equations to solve it? Or should I use particular numbers?[/spoiler]
A certain basketball team that has played 2/3 of its games
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Given:Vincen 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
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.
Answer = D
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Brent
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Since 20 games (17 wins and 3 losses) represent 2/3 of the total games played, we can say:Vincen 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
(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.
Answer: D
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