A basketball team won its first 8 games of the season, and then won 25

Question

A basketball team won its first 8 games of the season, and then won 25% of its remaining games. If it won 50% of its games for the entire season, how many games did it play that season?

A. 12
B. 16
C. 18
D. 20
E. 24

pushpitkc · Answer

Let the remaining games played by the basketball team be x

Since the team wins the first 8 games and 1/4rth of the remaining games, the equation framed it as follows :
 \frac{8 + .25x}{8 + x} = \frac{1}{2}

16 + .5x = 8 + x

0.5x = 8  
Multiplying by 2,  x = 16

The total games played by the basketball team is 8+16 =  24(Option E)

sashiim20 · Answer

Basketball team won its first  8  games of the season.

Let the remaining games be  = x

Then won  25  %   of its remaining games.  => 25  %   of  x = \frac{25}{100} * x = \frac{1}{4}x

Total games played in season  = 8 + x

Total games won  = 8 + \frac{1}{4}x  ---------- (i)

Team won  50  %  of its games for the entire season.  => 50  %  of  (8 + x) = \frac{50}{100} * (8+x) = \frac{1}{2} (8+x)  --------- (ii)

Equating (i) and (ii), we get;

8 + \frac{1}{4}x = \frac{1}{2} (8 + x) = \frac{1}{2} * 8 + \frac{1}{2}x

8 + \frac{1}{4}x = 4 + \frac{1}{2}x

\frac{1}{2}x - \frac{1}{4}x = 8 - 4

\frac{(2x-1x)}{4} = 4

\frac{1}{4}x = 4

x = 4*4 = 16

Total games played in season  = 8 + x = 8 + 16 = 24

Answer (E)...

Deepak@GMAT · Answer

eqn :-

=> 8 + 1/4*(x-8)=1/2 * x

=> x = 24

x total number of games

gracie · Answer

let t=total games
8+(t-8)/4=t/2
t=24
E

Bounce1987 · Answer

8+x/4/8+x=1/2
32+x/4/8+x=1/2
32+x/4(8+x)=1/2
32=2x
x=16
Answer=16+8=24=E

Mo2men · Answer

Let X = total games

8 + 1/4 (X - 8) = 1/2 X

8 + (1/4) X - 2= 1/2 X

1/4 X = 6...........X =24

Answer: E

nkmungila · Answer

8+x/4-2 = x/2
So X= 24

gps5441 · Answer

We can use answer choices as well.
Let us start from the middle.
Total games played is=18
50% won=9
First 8 games won then game left is 1 now this cannot be 25% of the rest of the 25% games won.
Let us take a higher no.
Let total no of games Played=24
50% of games won=12
first 8 games won left is 4.(Total games won is 12)
Rest of the games left is 16(24-8) and 25% of 16 is 4. Total games won -=8+4=12 Answer.

KB04 · Answer

I think this question can be solved by weighted averages.

Let the # of the remaining games be R then

8 + 1/4 (R) = 1/2 (R+8)

Solve for R.
After solving, R = 16
Total = R+8 = 16+8 = 24 = E

adityasuresh · Answer

A basketball team won its first 8 games of the season, and then won 25% of its remaining games. If it won 50% of its games for the entire season, how many games did it play that season?

A. 12
B. 16
C. 18
D. 20
E. 24

We could use alligation
A1 = 100 (Win % = 100 as the basketball team won all of its first 8 games)
A2 = 25(Win % = 25 for remaining games - stem)
Aavg = 50%(stem)
 A2-Aavg/Aavg-A1  =  25-50/50-100  =  1/2 
 1/3 (Total) = 8
Total = 24

E

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A basketball team won its first 8 games of the season, and then won 25

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A basketball team won its first 8 games of the season, and then won 25

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards