Three sisters have an average (arithmetic mean) age of 25 years and a median age of 24 years...

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Manhattan Prep

Three sisters have an average (arithmetic mean) of 25 years and a median of 24 years. What is the minimum possible age, in years, of the oldest sister?

A. 24
B. 25
C. 26
D. 27
E. 28

OA D

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Manhattan Prep

Three sisters have an average (arithmetic mean) of 25 years and a median of 24 years. What is the minimum possible age, in years, of the oldest sister?

A. 24
B. 25
C. 26
D. 27
E. 28

OA D

Solution:

Since 3 sisters have an average age of 25 years, the sum of their ages is 75.

To minimize the age of the oldest sister, we want to maximize the ages of the two youngest sisters. Since the median is 24, the two youngest sisters could both be 24 years old.

Thus, the minimum possible age of the oldest sister is 75 - (24 + 24) = 75 - 48 = 27.

Answer: D