Thirty different integers are chosen at random from the integers 1-50 inclusive. Which of the following statements must be true?

I. At least on of the integers chosen is odd

II. At least one of the integers chosen is a multiple of 5

III. At least on one of the integers choses is less than 15

A) I

B) II

C) I and II

D) I and III

E) I, II and III

There are only 25 even integers in that range, so **I** is true.

There are 10 multiples of 5 in that range, so it is possible to pick 30 numbers that are not multiples of 5, so **II** doesn’t have to be true.

There are 14 integers less than 15, so **III** also doesn’t have to be true. One could pick 30 integers that are all greater than 15 and less than 50.

The answer is **A**.