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How many positive integers less than 70 are multiples of eit
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06 Apr 2020, 05:45
06 Apr 2020, 05:45
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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
A. 17
B. 18
C. 23
D. 30
E. 35
Kudos for the right answer and explanation
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: How many positive integers less than 70 are multiples of eit
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06 Apr 2020, 05:49
06 Apr 2020, 05:49
2
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
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 = 40
At 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 = 10
So, 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
Re: How many positive integers less than 70 are multiples of eit
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28 Aug 2021, 08:18
28 Aug 2021, 08:18
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