How many 2-digit positive integers are divisible by 4 or 9?

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how many 2-digit positive integers are divisible by 4 or 9?

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How many 2-digit positive integers are divisible by 4 or 9?

To find out how many 2-digit positive integers are divisible by 4 or 9, we can analyze each case separately and then add up the results.

  1. Divisible by 4:
    A number is divisible by 4 if the last two digits of the number form a multiple of 4. The multiples of 4 between 10 and 99 are 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, and 92. Counting these numbers, we have a total of 21 2-digit positive integers that are divisible by 4.

  2. Divisible by 9:
    A number is divisible by 9 if the sum of its digits is a multiple of 9. Considering the 2-digit positive integers, we have the following numbers that satisfy this condition: 18, 27, 36, 45, 54, 63, 72, 81, and 90. Counting these numbers, we have a total of 9 2-digit positive integers that are divisible by 9.

Now, to find the total number of 2-digit positive integers that are divisible by 4 or 9, we need to add the results from the two cases.
21 (divisible by 4) + 9 (divisible by 9) = 30.
Therefore, there are 30 2-digit positive integers that are divisible by 4 or 9.

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