Question : The average of eight consecutive odd numbers is 48. Find the sum of the fifth and seventh numbers.
Option 1: 102
Option 2: 86
Option 3: 89
Option 4: 90
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Correct Answer: 102
Solution :
Given that the average of eight consecutive odd numbers is 48.
Let the eight consecutive odd number be $x, (x + 2), (x + 4), (x + 6), (x + 8), (x + 10), (x + 12), (x + 14)$
Average of eight consecutive odd numbers = 48
⇒ $\frac{x + (x + 2) + (x + 4) + (x + 6) + (x + 8) + (x + 10) + (x + 12) + (x + 14)}{8} = 48$
⇒ $(8x + 56) = 384$
⇒ $8x = 328$
⇒ $x = 41$
$\therefore$ 5th number = 41 + 8 = 49
And, 7th number = 41 + 12 = 53
⇒ Total = 49 + 53 = 102
Hence, the correct answer is 102.
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