Bunuel wrote:
What is the smallest of six consecutive odd integers whose average (arithmetic mean) is x + 2?
A. x - 5
B. x - 3
C. x - 1
D. x
E. x + 1
We can let the first (or smallest) odd integer = n, and thus we have:
n, n + 2, n + 4, n + 6, n + 8, and n + 10 as the six consecutive odd integers.
Since the average of terms in an evenly spaced set is (first number + last number)/2:
(n + n + 10)/2 = x + 2
2n + 10 = 2x + 4
2n = 2x - 6
n = x - 3
Answer: B
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