Question

How many two digit numbers have one odd digit and one even digit?

Answer 1

There are 36 two-digit numbers that have one odd digit and one even digit, considering all combinations of odd and even digits while excluding the cases where the digit 0 would be in the tens place.

Step-by-step explanation:

The question asks how many two-digit numbers contain one even and one odd digit. To find the answer, we consider all the possible combinations of one even and one odd digit.

For a two-digit number, the tens place can be occupied by an even digit 2, 4, 6, or 8 and an odd digit 1, 3, 5, 7, or 9. The units place can be occupied by the opposite parity digit from the tens place.

If the tens place is even, there are 4 possible even digits that can be placed there and 5 possible odd digits for the units place, creating a total of 4 × 5 = 20 combinations. However, we must also consider the possibility of the tens place being odd, which also results in 5 × 4 = 20 combinations, making a total of 20 + 20 = 40 two-digit numbers with one even and one odd digit.

However, we must exclude the case where the even digit is 0 because it would not form a two-digit number. With 0 as a units digit and with 4 possibilities for the tens place (1, 3, 5, 7, 9), we would have to subtract those 4 instances from the total, which gives us 40 - 4 = 36.

Therefore, 36 two-digit numbers have one odd digit and one even digit.

Answer 2

So there are 45 positive 2 digit numbers with one odd and one even digit, starting with 10 and going up to 98. There are 90 positive 2 digit numbers, from 10 to 99. Of these, 50 (from 10-19 up to 90-99) start with an odd digit and 40 (from 20-29 up to 80-89) start with an even digit. Of the 50 that start with an even digit, half of them (25) have an odd second digit, and of the 40 that start with an even digit, 20 have an odd second digit. So there are 45 positive 2 digit numbers with one odd and one even digit, starting with 10 and going up to 98.

For each of these, there is a negative counterpart. So there are a total of 90 when both positive and negative numbers are considered.