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# If a basketball team scores an average (arithmetic mean) of x points

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Re: If a basketball team scores an average (arithmetic mean) of x points [#permalink]
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The sum of points for the first n games will be (Average points for n games * no. of games(n)): xn
So, if y points have been added, the total no. of points in (n+1) games will be [xn + y];

Average of n+1 games = [xn + y]/[n+1]

Ans is (A)
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Re: If a basketball team scores an average (arithmetic mean) of x points [#permalink]
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If a basketball team scores an average (arithmetic mean) 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)

Problem Solving
Question: 116
Category: Arithmetic Statistics
Page: 76
Difficulty: 550

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Average = total/number

x = total/number

Instead of creating a variable t for total, you should use xn.

Then the new score is y, so the new total is xn (prior total) + y (increment)

The new total number is n+1.

(xn+y)/(n+1)
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Re: If a basketball team scores an average (arithmetic mean) of x points [#permalink]
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After reading the question, analyze the givens.

Let X = points average current games
Let N = number of current games
Y = points of next game
N + 1 = Number of current games plus the next game

Sum points / Total Games = Average
Average x Total Games = Sum points
Average of current games x total current games + points of next game / total number of games including next game

Therefore,

(X x N) + Y / N + 1

(A)
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Re: If a basketball team scores an average (arithmetic mean) of x points [#permalink]
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

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Re: If a basketball team scores an average (arithmetic mean) of x points [#permalink]
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Quote:

If a basketball team scores an average (arithmetic mean) 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) $$\frac{(nx + y)}{(n + 1)}$$

(B) $$x + \frac{y}{(n + 1)}$$

(C) $$x + \frac{y}{n}$$

(D) $$\frac{n(x + y)}{(n + 1)}$$

(E) $$\frac{(x + ny)}{(n + 1)}$$

The sum of points for n games is nx. If the team scores y points in the next game the new average is:

(nx + y)/(n + 1)

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Re: If a basketball team scores an average (arithmetic mean) of x points [#permalink]
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Re: If a basketball team scores an average (arithmetic mean) of x points [#permalink]
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