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20 Dec 2024, 21:52
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Statement (1): The 5 players scored a total of 20 goals. If each player scored at least 1 goal, we can distribute the goals as follows:
- Worst-case scenario (for our question): We want to distribute the goals as evenly as possible to minimize the chance of someone scoring 5 or more.
- Example: 4, 4, 4, 4, 4. This totals 20 goals, and no one scored 5 or more.
- However, consider 1, 2, 3, 6, 8. This also totals 20 goals, and two players scored more than 5.
Statement (2) says that no two of the 5 players scored the same number of goals. Since each player scored at least one goal, the minimum number of goals scored by the five players would be 1, 2, 3, 4, and 5. This totals 1 + 2 + 3 + 4 + 5 = 15 goals.
The key is that to have five different positive integer scores, one of those scores must be at least 5. There's no way to have five different positive integers where the largest is less than 5 (e.g., you can have 1, 2, 3, 4, but you can't have five distinct positive integers all less than 5).
Therefore, statement (2) alone is sufficient to conclude that at least one player scored at least 5 goals.
20 Dec 2024, 22:06
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On analyzing option (A) first if the total number of goals scored by the 5 members in the team are 20 & each player scored at least one goal
There are multiple possibilities of at least one person scoring at least 5 goals as one condition could 1,2,3,4,10 goals to get to 20 goals.
But there is one possibility that all the members scored the same number of goals which would amount to 20/5=4 goals per person. If everyone on the team scored 4 goals then it's not sufficient to answer that one member scored at least 5 goals.
Since this one condition makes the situation ambiguous (A) is not sufficient to answer this question & can be eliminated as can option (D).
On analyzing option (B) alone if each person scored at least one goal & no one scored the same number of goals then the basic possible condition that satisfies this situation is that the members scored 1,2,3,4,5 goals. Since we will always have one person score at least 5 goals & can extend this furthr to other possibilities,B is sufficient.
Hence the answer to this given question is option (B)
There are multiple possibilities of at least one person scoring at least 5 goals as one condition could 1,2,3,4,10 goals to get to 20 goals.
But there is one possibility that all the members scored the same number of goals which would amount to 20/5=4 goals per person. If everyone on the team scored 4 goals then it's not sufficient to answer that one member scored at least 5 goals.
Since this one condition makes the situation ambiguous (A) is not sufficient to answer this question & can be eliminated as can option (D).
On analyzing option (B) alone if each person scored at least one goal & no one scored the same number of goals then the basic possible condition that satisfies this situation is that the members scored 1,2,3,4,5 goals. Since we will always have one person score at least 5 goals & can extend this furthr to other possibilities,B is sufficient.
Hence the answer to this given question is option (B)
20 Dec 2024, 22:12
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(1) Together, the 5 players scored a total of 20 goals during the tournament.
5 players can score 4 goal each; or 1 player score 3 goal, 3 players score 4 goals, 1 player score 5 goals. So we don't know the answer
(2) No two of the 5 players scored the same number of goals.
The lowest case would be as follows for 5 players: A 1 goal, B 2 goals, C 3 goals, D 4 goals, E 5 goals. So at least 1 player must score at least 5 goals.
Answer: B
5 players can score 4 goal each; or 1 player score 3 goal, 3 players score 4 goals, 1 player score 5 goals. So we don't know the answer
(2) No two of the 5 players scored the same number of goals.
The lowest case would be as follows for 5 players: A 1 goal, B 2 goals, C 3 goals, D 4 goals, E 5 goals. So at least 1 player must score at least 5 goals.
Answer: B
