Question : The average of three consecutive odd numbers is 52 more than $\frac{1}{3}$rd of the largest number. What is the smallest of these numbers?
Option 1: 79
Option 2: 75
Option 3: 81
Option 4: 77
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Correct Answer: 77
Solution :
Let $(x–2), x$ and $(x+2)$ be the 3 consecutive odd numbers.
Average of AP with an odd number of terms = middle term
⇒ Average = $x$
Since the average of 3 consecutive odd numbers is 52 more than $\frac{1}{3}$rd of the largest number,
$x = 52+\frac{(x+2)}{3}$
⇒ $3x = (52×3)+(x+2)$
⇒ $2x = 158$
⇒ $x = 79$
Smallest number = 79 – 2 = 77
Hence, the correct answer is 77.
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