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

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AAPL: Moderator; Posts: 2632; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Mon Sep 17, 2018 8:14 am

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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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Source: Beat The GMAT — Problem Solving | Mon Sep 17, 2018 8:14 am

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Mon Sep 17, 2018 8:35 am

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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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Sep 17, 2018 9:57 am

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

Brent Hanneson - Creator of GMATPrepNow.com

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Mon Sep 17, 2018 3:12 pm

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 [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8136; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Tue Sep 18, 2018 5:50 pm

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
[email protected]

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