Question 9. How many positive integers between 100 and 300 have only odd digits? We can start off by listing out odd digits, which will be 1, 3, 5, 7, and 9. We know that we can exclude any number above 200, since if a number is 200, it already has an even digit, the 2, so we will only be looking at numbers from 100 to 199. Let's start off by segregating them into the tens spots, so we have numbers at 100 and 101, 102, and so on, then 110, 11, 12, so on, and we can list all of these like so. We can immediately remove some of these, such as any number that is 120-something already has an even digit, and this is true of half of these numbers, so we can eliminate them. Now, starting off with 110, we list out all the numbers that fit in 110, 111, 112, 113, 114, 15, 16, 17, 18, and 19. Again, we notice that we can cross out half of these numbers, since they have even digits, like so. Now, without writing it out for each of the next examples, we can make markers, like so. You can write it on your paper as 131, 133, 135, 137, 139, 151, and so on, but instead, we just have dots marking it. To find the answer to our question, we just have to count the amount of instances of this, and when we do this, we get our answer, which is A, 25.

positive integers

odd digits

100 to 199

counting method

elimination