Given:
The sum of eight consecutive odd numbers = 656
The average of four consecutive even numbers = 87
Calculation:
Let the 8 consecutive odd numbers be x, (x + 2), (x + 4), (x + 6), (x + 8), (x + 10), (x + 12) and (x + 14)
x + (x + 2) + (x + 4) + (x + 6) + (x + 8) + (x + 10) + (x + 12) + (x + 14) = 656
⇒ 8x + 56 = 656
⇒ 8x = 600
⇒ x = 75
Smallest odd number = 75
Let the 4 consecutive even numbers be x, (x + 2), (x + 4) and (x + 6)
x + (x + 2) + (x + 4) + (x + 6) = 4 × 87
⇒ 4x + 12 = 348
⇒ 4x = 336
⇒ x = 84
⇒ Second-largest even number = x + 4 = 88
∴ The sum of the smallest odd number and second-largest even number = 75 + 88 = 163