I am thinking of a counting number that is a multiple of 5, but not of 2 or of 3. It has either 2 digits or 3 digits, and no digit is greater than 5. How many numbers could I be thinking of?
25, 35, 55, 65, 85,
Continue from there.
To find the answer to this question, we need to break it down into steps:
Step 1: Identify the counting numbers that are multiples of 5.
To do this, we can start counting from 5, and keep adding 5 to get the next multiple of 5: 5, 10, 15, 20, 25, 30, 35, 40, etc.
Step 2: Determine which of these multiples of 5 are not multiples of 2 or 3.
To do this, we can go through the list of multiples of 5 we obtained in step 1 and eliminate any numbers that are also multiples of 2 or 3. For example, multiples of 2 are numbers that can be divided evenly by 2, and multiples of 3 are numbers that can be divided evenly by 3.
Step 3: Count the numbers with 2 or 3 digits that do not have any digit greater than 5.
We need to find the numbers from the remaining list in step 2 that have either 2 or 3 digits and do not have any digit greater than 5. Counting them will give us the final answer.
Note: Since we are given the condition that no digit is greater than 5, we can exclude numbers that contain the digit 6, 7, 8, or 9.
By following these steps, you can systematically narrow down the possibilities and determine the number of counting numbers that meet the given conditions.