Question : There are 32 consecutive natural numbers. The average of the first 13 numbers is $x$. What is the average of the next 19 numbers?
Option 1: $x+15$
Option 2: $x+16$
Option 3: $x+17$
Option 4: $x+18$
Correct Answer: $x+16$
Solution :
The average of a set of consecutive natural numbers is the middle number if the count of numbers is odd, or the average of the two middle numbers if the count is even.
In this case, the average of the first 13 numbers is $x$, which is also the 7th number in the set.
The average of the next 19 numbers will be the 10th number in that set, which is also the (13 + 10) = 23rd number in the original set of 32 numbers.
Since the numbers are consecutive, the 23rd number will be $x + 16$.
Hence, the correct answer is $x + 16$.
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