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02 Jan 2018, 01:29
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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84% (02:15) correct
16%
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A soccer team scores x goals the first game then averages twice as many goals for the next 5 games. The team averages two goals less than the average (arithmetic mean) of the previous 5 games over their next four games. How many goals will the team have scored after 10 games?
A. 19x − 8
B. 15x
C. 12x
D. 19x/10
E. 27x
A. 19x − 8
B. 15x
C. 12x
D. 19x/10
E. 27x
02 Jan 2018, 15:10
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Bunuel
Attachment:
soccergoals.png [ 11.82 KiB | Viewed 3464 times ]
There are three groups of games.
Each group has
• A, an average number of goals
• n, a number of games and
• S, Sum (A * n), total number of goals for that group
There are 1 + 5 + 4 = 10 games
Total number of goals? Sum the sums for each group
\(A*n = S\)
1) first game: team scores x goals
A = x, n = 1, S = x
2) next 5: average is twice that of first game
A = 2x, n = 5, S = 10x
3) next 4: 2 goals less than average for the previous 5 games
A = 2x - 2, n = 4
S = 4(2x - 2) = 8x - 8
The total number of goals after 10 games: sum the sums
\(x + 10x + 8x - 8\) =
\(19x - 8\)
Answer
Assign values
• Let first week = 1 goal
1 game * average of 1 goal = 1 goal total
• Next 5 weeks, team averages twice as many goals as the first week
5 games * average of 2 goals = 10 goals
• Next 4 weeks, team averages 2 less than average (arithmetic mean) of previous 5 games' average
4 games * average of 0 goals = 0 goals total
• Total number of goals scored after 10 games?
Number of games? 1 + 5 + 4 = 10
Total number of goals: (1 + 10 + 0) = 11 goals total
• Using x = 1, find the answer choice that yields 11 goals
Eliminate D (not an integer) and E immediately (it's huge)
A. 19x − 8: (19)(1) - 8 = 11. MATCH
B. 15x: (15)(1) = 15. NOT A MATCH
C. 12x (12)(1) = 12. NOT A MATCH
Answer
03 Jun 2020, 22:32
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Goal scored in 1 match = x goals
Goal scored in next 5 matches on avg. = 2x
Goal scored in next 4 matches = (Avg. of 5 matches) - 2
= 2*5*x/5
= 2x- 2
Total goal scored after 10 matches
= x+ 2x*5 + 4(2x-2)
= x+10x+8x-8
= 19x-8
IMO(A)
Goal scored in next 5 matches on avg. = 2x
Goal scored in next 4 matches = (Avg. of 5 matches) - 2
= 2*5*x/5
= 2x- 2
Total goal scored after 10 matches
= x+ 2x*5 + 4(2x-2)
= x+10x+8x-8
= 19x-8
IMO(A)
