There are four consecutive odd numbers, denoted by x₁, x₂, x₃, and x₄, and three consecutive even numbers, denoted by y₁, y₂, and y₃. The average of the odd numbers is six less than the average of the even numbers. Additionally, the sum of the three even numbers is 16 less than the sum of the four odd numbers. What is the average of x₁, x₂, x₃, and x₄?
Show answer & explanation
Correct answer: B
Explanation
Let four consecutive odd numbers = a, a + 2, a + 4, a + 6
And three consecutive even numbers = b, b + 2, b + 4
Average of odd numbers = a + 3
Average of even numbers = b + 2
a + 3 = b + 2 − 6
b = a + 7
3b + 6 = (4a + 12) − 16
3(a + 7) + 6 = 4a − 4
3a + 27 = 4a − 4
a = 31
Hence, four odd numbers = 31, 33, 35, 37
Their average = (31 + 33 + 35 + 37)/4 = 34