{0, 1, 2, 3, 4, . . . , 148, 149, 150} How many members of the above set are multiples of 3 but not multiples of 5? *

3, 6, 9, 12, 18, 21, 24, 27, 33, 36, 39, 42, 48, 51, 54, 57, 63, 66, 69, 72, 78, 81, 84, 87, 93, 96, 99, 102, 108, 111, 114, 117, 123, 126, 129, 132, 138, 141, 144, 147.

15,30,45, 60,75,90, 105, 120,135 and 150 are multiples of 5 and so they are not included.

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facundo3141592 facundo3141592 · Answer 2 · 2022-03-21T15:24:03+01:00

There are 40 numbers that are multiples of 3 but not multiples of 5 in the given set.

How many elements are multiples of 3 but not of 5?

The largest number on the set is 150, then we need to find by which number we need to multiply 3 to get that number:

150 = 3*k

150/3 = k = 50

This means that there are 50 + 1 multiples of 3 in that set (the extra 1 appears because 0 is also a multiple of 3).

Now, we need to remove the multiples of 5, so we start by removing the 0, because:

5*0 = 0

Now we just need to keep finding the multiples of 3 and 5.

We know that:

3*5 = 15

Then we need to keep adding 15 until we reach 150

0, 15, 30, 45, 60, 75, 90, 105, 120, 135, 150

All of these are multiples of both 3 and 5, and we need to remove these 11 numbers.

Then we can conclude that we have:

51 - 11 = 40 multiples of 3 but not multiples of 5 in the given set.

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