Question : The sum of three consecutive even numbers is 28 more than the average of these three numbers. Then the smallest of these three numbers is:
Option 1: 6
Option 2: 12
Option 3: 14
Option 4: 16
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Correct Answer: 12
Solution : Let $(x–2),x$ and $(x+2)$ be the 3 consecutive even numbers. ⇒ Sum = $(x–2)+x+(x+2) = 3x$ Average of AP with an odd number of terms = middle term ⇒ Average = $x$ Since the sum of three consecutive even numbers is 28 more than the average of these three numbers, $3x = 28+x$ ⇒ $2x = 28$ ⇒ $x = 14$ Smallest number $= (x - 2) = 14 - 2 = 12$ ⇒ The smallest number is $12$. Hence, the correct answer is 12.
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