The average of five natural numbers is 150. A particular number among

This is not a GMAT question. GMAT doesn't use the terminology of natural numbers.

Let the 5 natural numbers in increasing order be: a, b, b, b, a+100
Note that a < b < a+100

\(\frac{(a+b+b+b+a+100)}{5} = 150\)
\(2a + 3b = 650\)

Since a < b, let's find the point where a = b
2a + 3a = 650
a = 130 = b
But b must be greater than a. If we increase b by 1, we need to decrease a by 3 to keep the average same. But that decreases the largest number too, so increase b by another 1.
So a = 127, b = 132 give us the numbers as 127, 132, 132, 132, 227

Since b < a+100, let's find the point where b = a+100
2a + 3(a+100) = 650
a = 70, b = 170
But b must be less than a+100. If we decrease b by 1, we need to increase a by 3 to keep the average same. But that increases the largest number too, so decrease b by another 1.
So a = 73, b = 168 give us the numbers as 73, 168, 168, 168, 173

Values of a will be: 73, 76, 79, ....127 (Difference of 3 to make b a natural number)
This is an AP.
Last term = First term + (n - 1)*Common difference
127 = 73 + (n - 1)*3
n = 19
So the last term (a+100) will also take 19 distinct values.

Answer (B)

*Edited