This GMAT quant practice question is a problem solving question from statistics and averages. Concepts tested combines arithmetic mean and range of numbers.
The average of 5 positive integers is 40. i.e., the sum of these integers = 5 * 40 = 200
Let the least of these 5 numbers be x.
Because the range of the set is 10, the largest of these 5 numbers will be x + 10.
If we have to maximize the largest of these numbers, we have to minimize all the other numbers.
That is 4 of these numbers are all at the least value possible = x.
So, x + x + x + x + x + 10 = 200
Or x = 38.
So, the maximum value possible for the largest of these 5 integers is 48.
Choice D is the correct answer.