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oquiella: Master | Next Rank: 500 Posts; Posts: 164; Joined: Tue May 12, 2015 9:06 am; Thanked: 3 times

by oquiella » Sun Sep 27, 2015 6:25 pm

If a basketball team scores an average of x points per game for n games and then scores y points in its next game, what is the team's average score for the n + 1 games?

A. nx+y/n+1
B. x+ y/n+1
C. x+ y/n
D. n (x+y)/n+1
E. x+ny/n+1

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Source: Beat The GMAT — Problem Solving | Sun Sep 27, 2015 6:25 pm

JohnTran: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Sat Sep 05, 2015 7:10 pm; Thanked: 2 times

by JohnTran » Sun Sep 27, 2015 6:43 pm

My result is as below:
1. A team score an average of x points for n games. I use "A" as point sum for n games,so
A/n=x => A=n*x

2. Team scores x point in next game, so
(A+y)/(n+1)=new average
Replace A with above result, we got
(x*n+y)/(n+1)

I got the answer A

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Bullzi: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Thu May 28, 2015 1:13 am; Thanked: 5 times

by Bullzi » Sun Sep 27, 2015 6:47 pm

Hello,
This is how I could approach, I'll let the experts confirm if this approach is right..

Let
T - Total points gained after n games played
n (given) - Total games played
x (given) - average after n games

The above relation can be written as
Avg = (T/n) = x --> T = nx --> Eq 1

After n+1 games, the equation becomes,
Avg = (T+y)/(n+1) --> Eq 2
Substituting from Eq 1, Eq 2 becomes
(nx+y)/(n+1), so, answer choice A

Thanks
Bullzi

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GMAT/MBA Expert

[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] » Sun Sep 27, 2015 9:32 pm

Hi All,

This question can also be solved by TESTing VALUES.

We're told that a team scored an average of X points per game for the first N games, then scores Y points in the next game....

IF....
X = 2
N = 3
Y = 4

We have a total of (2)(3) + (4)(1) = 10 points scored over 4 games.

We're asked for the AVERAGE SCORE for all games. In this case, the average is 10/4 = 2.5

Although the original question does not include it, I assume that each numerator and each denominator is meant to have PARENTHESES around it...

Answer A: 10/4 = 2.5 This is a MATCH
Answer B: 6/4 = 1.5 NOT a match
Answer C: 6/3 = 2 NOT a match
Answer D: 18/4 = 4.5 NOT a match
Answer E: 14/4 = 3.5 NOT a match

Final Answer: A

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

Contact Rich at [email protected]

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GMAT/MBA Expert

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 28, 2015 11:10 am

Rich and others have nicely demonstrated the two methods (Algebraic and Input-Output) for solving a question type I call Variables in the Answer Choices.
If you'd like more information on these approaches, we have some free videos:
- Variables in the Answer Choices - https://www.gmatprepnow.com/module/gmat- ... /video/933
- Tips for the Algebraic Approach - https://www.gmatprepnow.com/module/gmat- ... /video/934
- Tips for the Input-Output Approach - https://www.gmatprepnow.com/module/gmat- ... /video/935

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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aorrick: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Sun Sep 27, 2015 7:22 am; GMAT Score:790

by aorrick » Wed Oct 07, 2015 11:43 am

I'm shocked that anyone actually finishes the test taking the advice on this website. x points per game for n games is nx points and thus nx + y points for n+1 games for an average of (nx + y)/(n+1). This is not a math test. Students who think are supposed to write down equations and solve them are the ones who score poorly. 3/4 of the quant can be answered in your head in 20 seconds without doing anything. Advice from a 790 scorer who wrote nothing down for at least 30 of the quant problems.

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Wed Oct 07, 2015 11:51 pm

Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

If a basketball team scores an average of x points per game for n games and then scores y points in its next game, what is the team's average score for the n + 1 games?

A. nx+y/n+1
B. x+ y/n+1
C. x+ y/n
D. n (x+y)/n+1
E. x+ny/n+1

Since the average scores of n games is x, the total scores of n games is nx. After one more game with y points the total score is nx+y and the total number of games is n+1. So the average score of n+1 games is (nx+y)/(n+1). So the answer is A.

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