Three sisters have an average (arithmetic mean) age of 25

AAPL wrote:Manhattan Prep

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

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

If the average age is 25, we can write: (sum of all 3 ages)/3 = 25
This means, the sum of all 3 ages = 75

If the median is 24, then we can express the ages in ascending order as follows: __ , 24, __

Since the sum of the ages is 75, we can MINIMIZE the age of the oldest girl by MAXIMIZING the age of the youngest girl.
Well, the youngest girl cannot be older than the median age (24), but the "youngest" girl can also be 24 (so there are 2 youngest sisters)
We get: 24, 24, __

Finally, since the sum of all 3 ages = 75, the oldest girl must be 27 years old.

Answer: D

Cheers,
Brent

AAPL wrote:Manhattan Prep

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

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