This GMAT quant practice question is a problem solving question from statistics and averages. Concepts tested combines arithmetic mean and range of numbers.

#### Question: If the average of 5 positive integers is 40 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers?

- 50
- 52
- 49
- 48
- 44

#### Video Explanation

Scroll down for explanation text#### Explanatory Answer

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.

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