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Math Expert
Joined: 02 Sep 2009
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07 Jul 2018, 09:51
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Difficulty:

25% (medium)

Question Stats:

73% (01:27) correct 27% (00:40) wrong based on 22 sessions

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Going in to the last game of his basketball season, Adrian had averaged 24 points per game. In his last game, he scored 50 points, bringing his average to 26 points per game for the season. How many games did Adrian play that season?

A. 12
B. 13
C. 14
D. 15
E. 16

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07 Jul 2018, 10:35
Bunuel wrote:
Going in to the last game of his basketball season, Adrian had averaged 24 points per game. In his last game, he scored 50 points, bringing his average to 26 points per game for the season. How many games did Adrian play that season?

A. 12
B. 13
C. 14
D. 15
E. 16

Sum of games played before last game = S
Number of games played before final game= n
S/n = 24 or S=24n

After going to his last game we have
(S+50)/(n+1)=26
Substituting S=24n we get
24n+50=26n+26
2n=24
n=12
Since we denoted "n" as the number of games before final game his total number of games played for the whole season would be - n+1=12+1=13.
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07 Jul 2018, 10:50
Bunuel wrote:
Going in to the last game of his basketball season, Adrian had averaged 24 points per game. In his last game, he scored 50 points, bringing his average to 26 points per game for the season. How many games did Adrian play that season?

A. 12
B. 13
C. 14
D. 15
E. 16

Let the no of games played by Adrian be x before the last game.

So, the total points earned=24x
New average=26 when he played the last game
Total points scored=24x+50
So, $$\frac{24x+50}{x+1}=26$$
Or, 24x+50=26x+26
Or, 2x=24
Or, x=12
Total no of games played= no of games played by Adrian be x [u]before the last game+1=x+1=12+1=13
Ans. (B)
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Joined: 02 Aug 2009
Posts: 6258

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07 Jul 2018, 10:57
Bunuel wrote:
Going in to the last game of his basketball season, Adrian had averaged 24 points per game. In his last game, he scored 50 points, bringing his average to 26 points per game for the season. How many games did Adrian play that season?

A. 12
B. 13
C. 14
D. 15
E. 16

Let there be x matches

three ways

1) logical....
Increase in avg of 2 for x games means 2x points
50 points are 24 points more than the new average..
so 2x=24.....x=12
and the 13th is the one in which 50 points were scored
ans 13

2) Algebraic

24 avg for x games .. total points = 24x
new total = 24x+50
new number of games = x+1
avg = $$\frac{24x+50}{x+1}=26................24x+50=26x+26..................2x=24........x=12$$
so games = 12+1=13

3) weighted average method

x games worth 24 and 1 game worth 50
average 26
so $$\frac{x}{1}=\frac{(50-26)}{(26-24)}\frac{24}{2}=12$$
so x+1=12+1=13

B
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07 Jul 2018, 11:08
Bunuel wrote:
Going in to the last game of his basketball season, Adrian had averaged 24 points per game. In his last game, he scored 50 points, bringing his average to 26 points per game for the season. How many games did Adrian play that season?

A. 12
B. 13
C. 14
D. 15
E. 16

$$24G + 50 = (G +1)26$$

Or, $$24G + 50 = 26G + 26$$

Or, $$2G = 24$$

Or, $$G = 12$$

So, Total Number of games played that season is 12 + 1 = 13 games,Answer must be (B)
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07 Jul 2018, 12:31
Increase in average by 2 points from 24 to 26 points. Hence a 2 point increase above average in every game.

The last game contributed (50 - 24) = 26 points to increase the average to 26.

Hence total # of games played = 26/2 = 13

Thanks,
GyM
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