The ages of three contestants in the Pascal Contest are 14 years, 9 months; 15 years, 1 month; and 14 years, 8 months. Their average (mean) age is
(A) 14 years, 8 months
(D) 14 years, 11 months
(B) 14 years, 9 months
(E) 15 years
(C) 14 years, 10 months
The ages of three contestants in the Pascal Contest are 14 years, 9 months; 15 years, 1 month; and 14 years, 8 months. Their average (mean) age is
(A) 14 years, 8 months
(B) 14 years, 9 months
(C) 14 years, 10 months
(D) 14 years, 11 months
(E) 15 years

## Solution 1

Consider one of the ages, say the youngest, as a base age. The other two contestants are one month and five months older respectively. Since $\frac{0+1+5}{3}=2$, this implies that the average age is two months greater than the youngest. This gives an average age of 14 years, 10 months.

## Solution 2

This second solution involves more calculation but gives the same correct answer. Since there are twelve months in a year, the age of the first contestant, in months, is $14 \times 12+9$ or 177 months. Similarly, the ages of the other two students would be 181 and 176 months. The average age would be $\frac{177+181+176}{3}$ or 178 months. The average age is then 14 years, 10 months because $178=12 \times 14+10$.

ANSWER: (C)