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# If a soccer team scores an average of x goals per game for n games, sc

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If a soccer team scores an average of x goals per game for n games, sc [#permalink]

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02 Jan 2018, 00:34
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89% (01:26) correct 11% (00:26) wrong based on 18 sessions

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If a soccer team scores an average of x goals per game for n games, scores an average of z goals for n-1 games, and scores an average of y goals in one game, what is the teams average goals for all the games?

A. $$\frac{(xn + y + zn - z)}{(2n)}$$

B. $$\frac{(x + y + x)}{(2n)}$$

C. $$x + \frac{(y + z)}{(2n)}$$

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

E. $$\frac{(xn + y + zn)}{(2n)}$$
[Reveal] Spoiler: OA

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If a soccer team scores an average of x goals per game for n games, sc [#permalink]

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02 Jan 2018, 04:13
Bunuel wrote:
If a soccer team scores an average of x goals per game for n games, scores an average of z goals for n-1 games, and scores an average of y goals in one game, what is the teams average goals for all the games?

A. (xn + y + zn - z)/(2n)
B. (x + y + x)/(2n)
C. x + (y + z)/(2n)
D. x/n + z/(n + 1) + y/(n - 1)
E. (xn + y + zn)/(2n)

Say, x = 2 & n = 2

z = 1 & n - 1 = n - 1 = 1

y = 0 in one game

Average =$$\frac{No. of goals}{No. of games}$$= $$\frac{2 + 1 + 0}{2 + 1 + 1}$$ = $$\frac{3}{4}$$ Target answer

Put these values in all equations one by one

Answer choice (C) gives the perfect result.
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Last edited by QZ on 03 Jan 2018, 23:28, edited 2 times in total.

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Re: If a soccer team scores an average of x goals per game for n games, sc [#permalink]

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03 Jan 2018, 11:48
Bunuel wrote:
If a soccer team scores an average of x goals per game for n games, scores an average of z goals for n-1 games, and scores an average of y goals in one game, what is the teams average goals for all the games?

A. (xn + y + zn - z)/(2n)
B. (x + y + x)/(2n)
C. x + (y + z)/(2n)
D. x/n + z/(n + 1) + y/(n - 1)
E. (xn + y + zn)/(2n)

Average goal for all games = $$\frac{TotalGoals}{TotalGames}$$ i.e.,

Overall Average = $$\frac{(Ave)(Qty) + (Ave)(Qty) + (Ave)(Qty)}{(TotalQty)}$$

Average goals scored = $$Ave = A$$
Number of games = $$Qty = n$$

1) average of x goals per game for n games
$$A_1 = x$$
$$n_1 = n$$
$$A_1*n_1 = S_1$$
$$xn = S_1$$

2) average of z goals for n-1 games
$$A_2 = z$$
$$n_2 = (n-1)$$
$$A_2*n_2 = S_2$$
$$z(n-1) = zn - z = S_2$$

3) an average of y goals in one game
$$A_3 = y$$
$$n_3 = 1$$
$$A_3*n_3 = S_3$$
$$y*1 = y = S_3$$

Total Goals: $$S_1 + S_2 + S_3 =$$
$$xn + (zn-z) + y = (xn + zn -z + y)$$

Total Games: $$n_1 + n_2 + n_3 =$$
$$n + (n-1) + 1 = (2n)$$

Overall Average: $$\frac{xn + zn - z + y}{2n}$$

[Reveal] Spoiler:
A

Assign values
This approach might save time if you have a good grasp of the algebra involved.
Let
n = 2
x = 1
z = 1
y = 1

1) "average of x goals per game for n games"
(1 * 2 ) = 2 goals
2) "average of z goals for (n-1) games"
(1 * 1) = 1 goal
3) "average of y goals for 1 game"
(1 * 1) = 1 goal

Overall total goals: (2 + 1 + 1) = 4
Overall total games: (2 + 1+ 1) = 4
Average goals per game: $$\frac{4}{4}=1$$

With assigned variables, find the answer that yields 1
If you check, the choice that yields 1 is

[Reveal] Spoiler:
A

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Re: If a soccer team scores an average of x goals per game for n games, sc [#permalink]

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03 Jan 2018, 17:08
Took me 4 mins to do this. Is there any shorter way?

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Re: If a soccer team scores an average of x goals per game for n games, sc [#permalink]

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03 Jan 2018, 17:31
Turkish wrote:
Took me 4 mins to do this. Is there any shorter way?

Yes. Average is always calculated in totals like ex : Avg Speed = Total Dist / Total time..
In this case Avg Goals = Total goals / Total Games

Total goals = goals in n matches + goals in n-1 matches + goals in 1 match = xn + z(n-1) + y

Total Games = n + n-1 + 1 = 2n

Put them together you get option A

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Re: If a soccer team scores an average of x goals per game for n games, sc [#permalink]

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03 Jan 2018, 19:21
Bunuel wrote:
If a soccer team scores an average of x goals per game for n games, scores an average of z goals for n-1 games, and scores an average of y goals in one game, what is the teams average goals for all the games?

A. (xn + y + zn - z)/(2n)
B. (x + y + x)/(2n)
C. x + (y + z)/(2n)
D. x/n + z/(n + 1) + y/(n - 1)
E. (xn + y + zn)/(2n)

Avr goals=(Total goals)/(Total games)
Total goals=x*n + z*(n-1) + y = (xn+zn-z+y)
Total games = n+n-1+1=2n
So avr goals = (xn+y+sn-z)/(2n)

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Re: If a soccer team scores an average of x goals per game for n games, sc   [#permalink] 03 Jan 2018, 19:21
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