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Going in to the last game of his basketball season, Adrian

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Going in to the last game of his basketball season, Adrian

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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

OA B.

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AAPL wrote:
Veritas Prep

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
The homogeneity nature of the average makes this problem trivial:
\[? = N\]
\[\sum\nolimits_{N - 1} = \,\,\,24\left( {N - 1} \right)\]
\[\sum\nolimits_N = \,\,\,26\,N\]
\[26N = 24\left( {N - 1} \right) + 50\,\,\,\,\,\, \Rightarrow \,\,\,\,2N = 26\,\,\,\,\, \Rightarrow \,\,\,\,? = N = 13\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

_________________
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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GMAT/MBA Expert

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AAPL 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 G = total number of games that Adrian played in the ENTIRE season

Going in to the last game of his basketball season, Adrian had averaged 24 points per game.
At this point, Adrian has played G-1 games
So, we can write: (total number of points in G-1 games)/(G-1) = 24
Multiply both sides of the equation by (G-1) to get: total number of points in G-1 games = 24(G-1)
Expand to get: total number of points in G-1 games = 24G - 24

In his last game, he scored 50 points...
We already know that total number of points in G-1 games = 24G - 24
So, TOTAL number of points for all G games = 24G - 24 + 50
Simplify to get: TOTAL number of points for all G games = 24G + 26

...bringing his average to 26 points per game for the season.
We can write: (total number of points in all G games)/G = 26
So, (24G + 26)/G = 26
Multiply both sides by G to get: 24G + 26 = 26G
Subtract 24G from both sides: 26 = 2G
Solve: G = 13

Answer: B

Cheers,
Brent

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Hi All,

We're told that going in to the last game of his basketball season, Adrian had averaged 24 points per game and in his last game, he scored 50 points (bringing his average to 26 points per game for the season). We're asked for the TOTAL number of games Adrian played that season. This question can be solved in a number of different ways, including with a 'logic shortcut' that doesn't take much more than a bit of Arithmetic to use.

We start with an unknown number of games - with an average score of 24 points/game. To raise this average by 2 (to 26 points/game), we essentially have to score 2 'extra' points for each game that has already been played - in addition to the 26 points that would need to be scored on the last game.

With 50 total points in the last game, that total can be broken down into one '26' and the remaining 24 points into 12 'groups of 2 points.' Thus, Adrian would have played.... 1+12 = 13 total games.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

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AAPL wrote:
Veritas Prep

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
We can let x = the number of games played in the season; thus, we have:

(24(x - 1) + 50)/x = 26

24x - 24 + 50 = 26x

26 = 2x

13 = x

Answer: B

_________________
Scott Woodbury-Stewart Founder and CEO

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