A football team averaged 35 points per game over the first

This topic has expert replies
Moderator
Posts: 7187
Joined: Thu Sep 07, 2017 4:43 pm
Followed by:23 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

A football team averaged 35 points per game over the first n games of the season. After scoring 28 points in the final game, their average was 34 points per game. How many games did the football team play?

A. 5
B. 6
C. 7
D. 9
E. 12

OA C

Source: Veritas Prep

User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pm
Thanked: 59 times
Followed by:33 members

by fskilnik@GMATH » Tue Oct 30, 2018 6:30 pm
BTGmoderatorDC wrote:A football team averaged 35 points per game over the first n games of the season. After scoring 28 points in the final game, their average was 34 points per game. How many games did the football team play?

A. 5
B. 6
C. 7
D. 9
E. 12
Source: Veritas Prep
$$? = n + 1$$
Let´s do it using alligation:


Image

$${1 \over {n + 1}} = {{35 - 34} \over {35 - 28}} = {1 \over 7}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = n + 1 = 7$$


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

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Tue Oct 30, 2018 10:10 pm
BTGmoderatorDC wrote:A football team averaged 35 points per game over the first n games of the season. After scoring 28 points in the final game, their average was 34 points per game. How many games did the football team play?

A. 5
B. 6
C. 7
D. 9
E. 12

OA C

Source: Veritas Prep
Say the team played n games before the final game.

Total points scored in n games = 35n
Total points scored in (n + 1) games, incl. final game = 35n + 28

=> Average score of (n + 1 ) games = (35n + 28) / (n + 1)

(35n + 28) / (n + 1) = 34 (given)

=> n = 6 => n + 1 = 7.

The correct answer: C

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: Manhattan Review India | Mehdipatnam GMAT Coaching | Madhapur GMAT Courses | Manhattan Review Hyderabad | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

Legendary Member
Posts: 2218
Joined: Sun Oct 29, 2017 2:04 pm
Followed by:6 members

by swerve » Wed Oct 31, 2018 9:34 am
35*n . . . sum of the points of the first n games.
n + 1 . . . total number of games

34 = (35*n + 28)/(n + 1)
34n + 34 = 35n + 28
n = 34 - 28 = 6
n + 1 = 7

Therefore, C is the correct answer.

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Wed Oct 31, 2018 10:26 am
BTGmoderatorDC wrote:A football team averaged 35 points per game over the first n games of the season. After scoring 28 points in the final game, their average was 34 points per game. How many games did the football team play?

A. 5
B. 6
C. 7
D. 9
E. 12
This is a weighted average/mixture problem.

Average score for the first N games = 35.
Score for the final game = 28.
Average score for the MIXTURE of all the games = 34.

Step-by-step instruction for the alligation approach:

Step 1: Plot the 3 averages on a number line, with the average for the first N games and that for the final game on the ends and the average for the mixture in the middle.
N 35----------------34----------------28 F

Step 2: Calculate the distances between the averages.
N 35--------1-------34--------6------28 F

Step 3: Determine the ratio in the mixture.
The ratio of N to F is equal to the RECIPROCAL of the distances in red.
N:F= 6:1

Since N:F = 6:1, the team played N=6 games with an average score of 35 and 1 final game with a score of 28, for a total of 7 games.

The correct answer is C.

Similar problems:

https://www.beatthegmat.com/ratios-fract ... 15365.html
https://www.beatthegmat.com/mean-t266852.html#684151
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 7222
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Fri Nov 02, 2018 4:03 pm
BTGmoderatorDC wrote:A football team averaged 35 points per game over the first n games of the season. After scoring 28 points in the final game, their average was 34 points per game. How many games did the football team play?

A. 5
B. 6
C. 7
D. 9
E. 12
Let n be the number of games the team played before the final game. We can create the equation:

34 = (35n + 28)/(n + 1)

34n + 34 = 35n + 28

6 = n

So the team played n + 1 = 7 games.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage