Question : The average of 4 consecutive numbers is 64.5. What is the largest number among these numbers?
Option 1: 62
Option 2: 60
Option 3: 67
Option 4: 66
Correct Answer: 66
Solution :
Given: The average of 4 consecutive numbers is 64.5.
Let the 4 numbers be $x$, $x+1$, $x+2$ and $x+3$, respectively.
The sum of the 4 numbers $=x+x+1+x+2+x+3=4x+6$
Use the formula, $\text{Average}=\frac{\text{Sum of all values}}{\text{Total number of values}}$
According to the question,
$\frac{4x+6}{4}=64.5$
⇒ $\frac{4x+6}{4}=64.5$
⇒ $4x+6=258$
⇒ $4x=252$
⇒ $x=63$
The largest number among these numbers = 63 + 3 = 66
Hence, the correct answer is 66.
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