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If the ages of three people are all different and their average age is 21 years, is the youngest person older than 13?
(1) The oldest person is 25 years old.
(2) One of the three people is 24 years old.
(1) The oldest person is 25 years old.
(2) One of the three people is 24 years old.
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12 Feb 2024, 09:27
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Official Solution:
If the ages of three people are all different and their average (arithmetic mean) age is 21 years, is the youngest person older than 13?
Note two things: a. since the average of three people is 21, the sum of their ages is 3*21 = 63 and b. the ages of three people are all different.
(1) The oldest person is 25 years old.
This implies that the sum of the ages of the two other younger people is 63 - 25 = 38. If the youngest person were 13 or younger, the other one must be 25 or older to reach the sum of 38. However, we are told that the oldest person is 25 years old, so the second oldest cannot be 25 or older. Therefore, the youngest person must be older than 13. Sufficient.
(2) One of the three people is 24 years old.
This is clearly insufficient. For example, consider the three ages to be (10, 24, 29) for a NO answer, and (14, 24, 25) for a YES answer. Not sufficient.
Answer: A
If the ages of three people are all different and their average (arithmetic mean) age is 21 years, is the youngest person older than 13?
Note two things: a. since the average of three people is 21, the sum of their ages is 3*21 = 63 and b. the ages of three people are all different.
(1) The oldest person is 25 years old.
This implies that the sum of the ages of the two other younger people is 63 - 25 = 38. If the youngest person were 13 or younger, the other one must be 25 or older to reach the sum of 38. However, we are told that the oldest person is 25 years old, so the second oldest cannot be 25 or older. Therefore, the youngest person must be older than 13. Sufficient.
(2) One of the three people is 24 years old.
This is clearly insufficient. For example, consider the three ages to be (10, 24, 29) for a NO answer, and (14, 24, 25) for a YES answer. Not sufficient.
Answer: A
General Discussion
17 Jul 2023, 08:23
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Let \(x + y + z = 63\) where x<y<z
(1) The oldest person is 25 years old.
Here we are told the value of \(z\), which means that \(x+y = 38\). To get the smallest possible value of \(x\), we maximize \(y\), which would be \(y = 24\). This means that the smallest possible value for \(x = 14\) which is greater than 13.
SUFFICIENT
(2) One of the three people is 24 years old.
This person cannot be the youngest person. If this person is the second eldest, \(x + z = 39\): To minimize \(x\), we maximize \(z\), which means that \(z = 38\) and \(y = 1\) making \(y<13\). However, it could also be that \(z = 25\) and \(y = 14\) where \(y>13\).
INSUFFICIENT
Answer A
(1) The oldest person is 25 years old.
Here we are told the value of \(z\), which means that \(x+y = 38\). To get the smallest possible value of \(x\), we maximize \(y\), which would be \(y = 24\). This means that the smallest possible value for \(x = 14\) which is greater than 13.
SUFFICIENT
(2) One of the three people is 24 years old.
This person cannot be the youngest person. If this person is the second eldest, \(x + z = 39\): To minimize \(x\), we maximize \(z\), which means that \(z = 38\) and \(y = 1\) making \(y<13\). However, it could also be that \(z = 25\) and \(y = 14\) where \(y>13\).
INSUFFICIENT
Answer A
