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
OA D
Source: Manhattan Prep
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A certain basketball team that has played 2/3 of its games
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BTGmoderatorDC
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A
B
C
D
E
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Games played thus far = 17 wins + 3 losses = 20.BTGmoderatorDC 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 these 20 games constitute 2/3 of the total number of games, we get:
20 = (2/3)T
60 = 2T
30 = T
Since the team must win at least 3/4 of these 30 games, it may lose at most 1/4 of these 30 games:
(1/4)30 = 7.5
Implication:
The total number of losses must be 7 or less.
Since the team has already lost 3 games, it may lose at most 4 more games.
The correct answer is D.
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BTGmoderatorDC 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
OA D
Source: Manhattan Prep
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.
Answer: D
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Scott@TargetTestPrep
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BTGmoderatorDC 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
OA D
Source: Manhattan Prep
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
Since x must be an integer, the largest integer less than or equal to 4.5 is 4.
Answer: D
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