How many odd 2-digit positive integers greater than 20 are there?

Answer 1

-18

Answer 2

You have 5 criteria with this question:

* The numbers must be integers. * The numbers must be positive. * The numbers must be > 20. * The numbers must be odd.

* The numbers must have only 2 digits. Let's list a few numbers. As an aside, ANY number greater than 20 is automatically positive. I will be listing only integers from here on, also.

(Criteria #1, 2, 3)

Positive integers > 20:

21, 22, 23, 24....

(Criteria #1, 2, 3, 4)

Positive odd integers > 20:

21, 23, 25, 27, 29, 31, 33, ...

(Criteria #1, 2, 3, 4, 5)

Positive, odd integers > 20, with only 2 digits:

21, 23, 25....31, 33, 35....41, 43, 45...51, 53, 55....91, 93, 95, 97, 99.

I have to stop listing numbers once I hit 99, because any integer > 100 will have at least 3 digits, and we only wanted 2.

Notice that for the range 20-30, 30-40, 40-50 etc there are how many odd numbers?

There are 5 odd numbers for every multiple of 10. This makes sense, since half are even and half are odd!

21, 23, 25, 27, 29 -- 5 numbers.

31, 33, 35, 27, 39 -- 5 numbers.

41, 43, 45, 47, 49 -- 5 numbers

51, 53, 55, 57, 59 -- 5 numbers

61, 63, 65, 67, 69 -- 5 numbers

71, 73, 75, 77, 79 -- 5 numbers

81, 83, 85, 87, 89 -- 5 numbers

91, 93, 95, 97, 99 -- 5 numbers

----------------------------------------

21 thru 99 odd -- 40 numbers.

We have 8 sets of numbers - 21 thru 29 odd, 31 thru 39 odd, ... 91 thru 99 odd.

Any number over 99 will have 3 digits, so it is excluded.

Any even number is excluded.

Any number < 20 is excluded.

So we're left with 8 sets of 5 numbers, or 40 odd numbers.

Your final answer is that there are 40 odd, two digit integers greater than 20.

Answer 3

40