Carcass wrote:
How many positive integers less than 70 are multiples of either 3 or 4 but not both?
A. 17
B. 18
C. 23
D. 30
E. 35
Kudos for the right answer and explanation
Multiples of 3: 3, 6, 9, . . . 69
We can write these values as follows: (
1)(3), (
2)(3), (
3)(3), . . . (
23)(3).
There are
23 multiples of 3
Multiples of 4: 4, 8, 12, . . . 68
We can write these values as follows: (
1)(4), (
2)(4), (
3)(4), . . . (
17)(4)
There are
17 multiples of 4
Sum =
23 +
17 =
40At this point we need to subtract all of the numbers that are divisible by 3 AND 4 both.
That is we want to subtract all of the numbers that are divisible by 12 within this range.
Multiples of 12: 12, 24, 36, . . . 60
We can write these values as follows: (
1)(12), (
2)(12), (
3)(12), . . . (
5)(12)
There are
5 multiples of 12
This means there are
5 multiples of 12 within the list of multiples of 3, and there are
5 multiples of 12 within the list of multiples of 4.
5 +
5 =
10So, the number of positive integers less than 70 that are multiples of either 3 or 4 but not both =
40 -
10 = 30
Answer: D
Cheers,
Brent