Three sisters, whose average age is 10, all have different ages. The average age of one pair of the sisters is 11, while the average age of a different pair is 12. What is the age of the eldest sister?
A 10 B 11 C 12 D 14 E 16
E
Since the average age of the three sisters is 10, their total age is 3 × 10 = 30. Since the average age of one pair of the sisters is 11, their total age is 2 × 11 = 22 and hence the age of the sister not included in that pairing is 30 − 22 = 8. Similarly, since the average age of a different pair of sisters is 12, their total age is 2 × 12 = 24 and hence the age of the sister not included in that pairing is 30 − 24 = 6. Therefore the age of the eldest sister is 30 − 8 − 6 = 16.
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