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

Question

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)}

AkshdeepS · Answer

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.

generis · Answer

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}

Answer 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

Answer  A

Turkish · Answer

Took me 4 mins to do this. Is there any shorter way?

laddaboy · Answer

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

Sent from my Moto G (5) Plus using  GMAT Club Forum mobile app

Phuonganhtran · Answer

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)
A is correct answer

bumpbot · Answer

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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

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