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08 Jan 2025, 05:40
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At a football championship, five players from the Spanish team each scored at least one goal. Did any one of the players score at least five goals during the tournament?
(1) The five players scored a total of twenty goals during the tournament.
(2) No two of the five players scored the same number of goals.
(1) The five players scored a total of twenty goals during the tournament.
(2) No two of the five players scored the same number of goals.
08 Jan 2025, 05:40
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Official Solution:
At a football championship, five players from the Spanish team each scored at least one goal. Did any one of the players score at least five goals during the tournament?
(1) The five players scored a total of twenty goals during the tournament.
If each of the five players scored 4 goals, then none of them scored 5 or more goals. However, if, for example, 4 players scored 2 goals each and the fifth player scored 12, then 1 player scored at least 5 goals. Not sufficient.
(2) No two of the five players scored the same number of goals.
Is it possible for all players to score fewer than 5 goals while still having no two players score the same number of goals? No. If the first four players scored 1, 2, 3, and 4 goals each (all less than 5), the fifth player, having to score a unique number of goals, must score at least 5. Thus, at least one player scored 5 or more goals. Sufficient.
Answer: B
At a football championship, five players from the Spanish team each scored at least one goal. Did any one of the players score at least five goals during the tournament?
(1) The five players scored a total of twenty goals during the tournament.
If each of the five players scored 4 goals, then none of them scored 5 or more goals. However, if, for example, 4 players scored 2 goals each and the fifth player scored 12, then 1 player scored at least 5 goals. Not sufficient.
(2) No two of the five players scored the same number of goals.
Is it possible for all players to score fewer than 5 goals while still having no two players score the same number of goals? No. If the first four players scored 1, 2, 3, and 4 goals each (all less than 5), the fifth player, having to score a unique number of goals, must score at least 5. Thus, at least one player scored 5 or more goals. Sufficient.
Answer: B
23 Jan 2026, 04:20
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