Question : What is the difference between the average of the first 148 even positive numbers and the average of the first 129 odd positive numbers?
Option 1: 21
Option 2: 20
Option 3: 23
Option 4: 19
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Correct Answer: 20
Solution :
The sum of the first $n$ even number $=n(n+1)$.
The sum of the first odd $n$ numbers $=n\times n$.
$\text{Average}=\frac{\text{Sum}}{\text{The total number}}$
The sum of the first 148 even numbers $=148(148+1)=148\times149$
The average of the sum of the first 148 even numbers $=\frac{148\times149}{148}=149$
The sum of the first 129 odd numbers $=129\times129$
The average of the sum of the first 129 odd numbers $=\frac{129\times129}{129}=129$
The difference between the average of the first 148 even positive numbers and the average of the first 129 odd positive numbers = 149 – 129 = 20
Hence, the correct answer is 20.
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