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

Question

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

(A) 7
(B) 6
(C) 5
(D) 4
(E) 3

MHIKER · Accepted Answer

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

KarishmaB · Answer

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.

Answer (D)

PareshGmat · Answer

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)

Answer = D

mvictor · Answer

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.

ScottTargetTestPrep · Answer

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.

Answer: D

BrentGMATPrepNow · Answer

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

Cheers,
Brent

Fdambro294 · Answer

Because the numbers are smaller and the Answer Choices are nice numbers, we can play with the answer choices until we find our answer.

The team has played 20 games so far. This represents 2/3rds of the Total Games. Therefore, there are 10 games to be played.

The Team wants to know the Maximum Number of games it can lose out of the 10 games and still win 3/4th of their Total Games

If the team wins 3/4 of the Total Games, this means the Team’s Ratio of Wins-to-Losses = 3-to-1

Wins : Losses : TOTAL Games = 3 : 1 : 4

Let W = wins out of the last 10 games

Let L = Losses our of the last 10 games

Where——-> W + L = 10

Requirement by the question:

(17 + W) / (3 + L) >/= 3/1

Test C- 5 losses (which means 5 wins)

(17 + 5) / (3 + 5) = 22/8 ——-> which is LESS THAN the Ratio of 3-to-1

However it is close. Let’s increase the wins slightly (NUM) and decrease the losses slightly (DEN)

-D- 4 losses (which means 6 wins)

(17 + 6) / (3 + 4) = 23/7 ——->

Which is definitely greater than the Ratio of 3-to-1

-D- is the Correct Answer.

Maximum game that can be lost in the last 10 games = 4

Posted from my mobile device

btsaami · Answer

Since he won 3/4th, he lost 1/4 of the total matches played.
With 17 wins and 3 losses, 2/3 of total matches= 20. Hence, total=30

For winning at least 3/4th of 30, he will lose matches which is less than or equal to 1/4 of 30.
Let l be the no. of matches lost in the remaining 1/3rd matches.
Therefore, 3+l<=1/4*30
3+l<=7.5
l<=4.5

Hence max value of l=4.

bumpbot · Answer

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

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