Bunuel wrote:
Of the people who donated money to a certain local theater last year, 1/4 donated $20 or less and 2/3 donated more than $20 but less than $1,000. If the average (arithmetic mean) amount donated by the people who donated more than $20 but less than $1,000 was $180, what was the average amount donated by the people who donated $1,000 or more?
(1) The average amount donated by the people who donated less than $1,000 was $132.
(2) The average amount donated by the people who donated more than $20 was $360.
Each person who donated is a member of exactly one of the following subgroups.
Subgroup 1: $20 or less
fraction of the whole = 1/4 = 3/12
average = a₁
Subgroup 2: between $20 and $1,000
fraction of the whole = 2/3 = 8/12
average = $180
Subgroup 3: $1,000 or more
fraction of the whole = 1 – 3/12 – 8/12 = 1/12
average = a₃
We need to answer the question:
a₃ = ?
Statement One Alone:=> The average amount donated by the people who donated less than $1,000 was $132.
Using the weighted arithmetic average formula, we could determine a₁:
[(3/12)a₁ + (8/12)180]/(3/12 + 8/12) = 132
However, we can’t answer the question. Statement one is not sufficient. Eliminate answer choices A and D.
Statement Two Alone:=> The average amount donated by the people who donated more than $20 was $360.
Using the weighted arithmetic average formula, we could determine a₃:
[(8/12)180 + (1/12)a₃]/(8/12 + 1/12) = 360
We could answer the question. Statement two is sufficient.
Answer: B