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

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

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

by AAPL » Mon Sep 17, 2018 8:14 am

Timer

00:00

Your Answer

Global Stats

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

OA B.

Quote

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 pm; Thanked: 59 times; Followed by:33 members

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

Quote

GMAT/MBA Expert

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

Quote

GMAT/MBA Expert

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

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

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