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29 Jul 2024, 08:04
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What is the median age of the athletes in Team A?
(1) No athlete's age in Team A is less than the average (arithmetic mean) age of the athletes in Team A.
(2) The mode age for the athletes in Team A is 21 years.
(1) No athlete's age in Team A is less than the average (arithmetic mean) age of the athletes in Team A.
(2) The mode age for the athletes in Team A is 21 years.
29 Jul 2024, 08:04
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Official Solution:
What is the median age of the athletes in Team A?
(1) No athlete's age in Team A is less than the average (arithmetic mean) age of the athletes in Team A.
Since no athlete's age is less than the average, it follows that no athlete's age is more than the average, suggesting that all ages in the team are the same. This implies that the average equals the median. However, the actual values remain unknown, so this statement is insufficient.
(2) The mode age for the athletes in Team A is 21 years.
The mode is the number that occurs the most frequently in a list. Hence, this statement simply says that the most common age in the team is 21 years. However, this does not mean that the median is also 21 years. For example, consider the list {21, 21, 22, 23, 24}, which has a mode of 21 but a median of 22. Therefore, this statement is insufficient.
(1)+(2) Since from (1) all ages in the team are the same, and from (2) the most frequent age is 21, it must be true that all athletes are 21 years old, making the median age also 21 years. Sufficient.
Answer: C
What is the median age of the athletes in Team A?
(1) No athlete's age in Team A is less than the average (arithmetic mean) age of the athletes in Team A.
Since no athlete's age is less than the average, it follows that no athlete's age is more than the average, suggesting that all ages in the team are the same. This implies that the average equals the median. However, the actual values remain unknown, so this statement is insufficient.
(2) The mode age for the athletes in Team A is 21 years.
The mode is the number that occurs the most frequently in a list. Hence, this statement simply says that the most common age in the team is 21 years. However, this does not mean that the median is also 21 years. For example, consider the list {21, 21, 22, 23, 24}, which has a mode of 21 but a median of 22. Therefore, this statement is insufficient.
(1)+(2) Since from (1) all ages in the team are the same, and from (2) the most frequent age is 21, it must be true that all athletes are 21 years old, making the median age also 21 years. Sufficient.
Answer: C
09 Oct 2024, 11:52
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I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Could you elaborate a bit more why if no athlete's age is less than the average, all their ages must be the average?
