hey_thr67 wrote:Average goals scored by 15 selected players in EPL is 16.Maximum goals scored by a player is 20 and minimum is 12. Goals scored by players is between 12 and 20.What can be maximum number of players who scored at least 18 goals ?
A: 10
B: 5
C: 9
D: 6
E: 11
Total number of goals = (number of players)(average number of goals) = 15*16 = 240.
Maximum goals scored by a player is 20 and minimum is 12.
The wording here is unclear.
My solution above assumed the following meaning: no player can score more than 20 goals, and no player can score fewer than 12 goals.
Anurag's solution above interprets the following meaning:
At least one player scores 20 goals, and at least one player scores 12 goals.
Assuming this interpretation, we could plug in the answers as follows.
When the question asks for the MAXIMUM possible value, the GREATEST answer choice is unlikely to be correct.
Thus, we should start with answer choice A, the second greatest answer choice.
To MAXIMIZE the number of players who score at least 18 goals, we must MINIMIZE the number of goals scored by every player besides the one who scores 20 goals.
Answer choice A: 10
Total goals scored by 1 player with 20 goals and 9 players with 18 goals each = 1*20 + 9*18 = 20+162 = 182.
Minimum number of goals scored by the remaining 5 players = 5*12 = 60.
Total goals = 182+60 = 242.
The total number of goals must be just a bit less, implying that the correct answer must be the next smallest option.
The correct answer is
C.
Answer choice C: 9
Total goals scored by 1 player with 20 goals and 8 players with 18 goals each = 1*20 + 8*18 = 20+144 = 164.
Minimum number of goals scored by the remaining 6 players = 6*12 = 72.
Total goals = 164+72 = 236, which is below the threshold of 240.
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