The mean and the median of nine distinct positive integers is 30. If the nine integers are such that their product is maximum, what is the product of the smallest and the largest integers?
My attempt:
In this problem, we are given that the mean and the median of a set of 9 distinct positive integers is 30. This means that the sum of the numbers is 9 * 30 = 270 and the number in the middle is 30.
This leaves us with 8 other numbers, which we can arrange in increasing (or decreasing) order.
But I am not sure how to continue with this problem, do I need to create some sort of range?
Here are the option of answers:
210
884
891
3422