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The sum of eight consecutive odd numbers is 656. The average of four consecutive even numbers is 87. What is the sum of the smallest odd number and second-largest even number?

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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

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