Question

How many whole numbers less than 100 are multiples of 3 but not multiples of 5?

Answer 1

Answer: There are 6 whole numbers less than 100 that are multiples of 3 but not multiples of 5: 15, 30, 45, 60, 75, and 90.

Step-by-step explanation:

To find the number of whole numbers less than 100 that are multiples of 3 but not multiples of 5, we need to determine the range of numbers that satisfy this condition.

First, let's consider the multiples of 3. The multiples of 3 are 3, 6, 9, 12, and so on. We can observe that every third number is a multiple of 3.

Next, let's consider the multiples of 5. The multiples of 5 are 5, 10, 15, 20, and so on. We can observe that every fifth number is a multiple of 5.

To find the numbers that are multiples of 3 but not multiples of 5, we need to find the common multiples of 3 and 5. This means we need to find the numbers that appear in both lists.

Let's compare the two lists:

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96

Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95

We can see that the numbers 15, 30, 45, 60, 75, and 90 appear in both lists.

Answer 2

There are 27 whole numbers less than 100 that are multiples of 3 but not multiples of 5, which is determined by listing the multiples of 3 and excluding any that are also multiples of 5.

Step-by-step explanation:

To find how many whole numbers less than 100 are multiples of 3 but not multiples of 5, we can list the multiples of 3 up to 99 and then eliminate the ones that are also multiples of 5. Multiples of 3 are 3, 6, 9, ..., up to 99. We can express the sequence as 3n where n ranges from 1 to 33 because 3 x 33 = 99. Now, we eliminate the multiples of 5 from this set. Multiples of 5 that also happen to be multiples of 3 are those where the multiple is a common multiple of 15 since 15 is the least common multiple of 3 and 5.

To find the multiples of 15 under 100, we divide 100 by 15, which gives us 6 with a remainder. Hence, there are 6 multiples of 15 under 100: 15, 30, 45, 60, 75, and 90. Subtracting these 6 from the 33 multiples of 3, we get 33 - 6 = 27. Therefore, there are 27 whole numbers less than 100 that are multiples of 3 but not multiples of 5.