What is the average (arithmetic mean) of n consecutive even integers?

We need to find What is the average (arithmetic mean) of n consecutive even integers?

============================================================

Theory

‣‣‣ Mean or Average = (Sum Of All The Numbers) / (Total Number Of Numbers)
‣‣‣ In case of consecutive terms mean = median = middle term = mean of first and last term.
‣‣‣ Range = Highest value - Lowest Value

============================================================

=> To find the average we need to find both the sum of values and the total number of values as we are given the total number as n

STAT 1: The range of the given integers is 20.

=> Range = Highest value - Lowest Value = 20 (given)
And we know that we have n consecutive even numbers
=> Highest value = Lowest Value + (n-1)*2 (Example if we have two consecutive even numbers, then highest value = lowest + 2 = Lowest + (2-1)*2)
=> Highest - Lowest value = (n-1)*2
=> (n-1)*2 = 20
=> n = 11

But we don't any of these 11 numbers to find their sum
=> NOT SUFFICIECT

STAT 2: When the given integers are arranged in the order of increasing magnitude, the average (arithmetic mean) of the first 3 terms is 12

Average of first three terms = middle term = second term = 12
=> First term is 12-2 = 10 and we can find all remaining terms
But, we don't know how many such terms are there
=> NOT SUFFICIECT

Combining, both of them we know both the number of terms and the actual terms.
=> We can find the Average of these n consecutive even integers.

=> SUFFICIENT

So, Answer will be C.
Hope it helps!

Watch the following video to learn How to Sequence problems