Question : 10 consecutive numbers are given. If the average of the two numbers given in the middle is 13.5, then what is the sum of the first 6 numbers?
Option 1: 58
Option 2: 55
Option 3: 67
Option 4: 69
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Correct Answer: 69
Solution :
Given that the average of two middle numbers in a list of 10 consecutive numbers is 13.5.
Let the smaller one be $x$.
Therefore, the next number is $x+1$.
The average of these two numbers is given by:
$⇒\frac{x + (x+1)}{2} = 13.5$
$\therefore x = 13$
Therefore, the two middle numbers are 13 and 14.
Since these are the 5th and 6th numbers in the list of 10 consecutive numbers.
The first number in the list will be 13 – 4 = 9
The sum of the first 6 numbers in this list = 9 + 10 + 11 + 12 + 13 + 14 = 69
Hence, the correct answer is 69.
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