The mean of a set of five different positive integers is 15. The median is 18. Find the maximum possible value of the largest of these five integers.

The median cant be 18 as this is physicaly impossible

35 (the sequence is 1,2,18,19,35)

Step-by-step explanation:

So you have 5 numbers a, b, 18, c, d ordered from low to high.

18 is given because it is the median.

If the mean is 15, the sum must be 75 (because 75/5=15).

d must be as high as possible, so the others must be as low as possible, but positive and different.

So let's say a=1 and b=2, we can't get any lower than that.

c can be no lower than 19, otherwise we'd lose the median.

That leaves for d = 75 - 19-18-2-1 = 35.

nice one