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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
How many positive integers less than 100 are neither multiples of 2 or
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18 Apr 2022, 09:56
18 Apr 2022, 09:56
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How many positive integers less than 100 are neither multiples of 2 or 3.
a) 30
b) 31
c) 32
d) 33
e) 34
a) 30
b) 31
c) 32
d) 33
e) 34
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: How many positive integers less than 100 are neither multiples of 2 or
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18 Apr 2022, 13:27
18 Apr 2022, 13:27
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GeminiHeat wrote:
How many positive integers less than 100 are neither multiples of 2 or 3.
a) 30
b) 31
c) 32
d) 33
e) 34
a) 30
b) 31
c) 32
d) 33
e) 34
Multiples of 2: 2, 4, 6, ..., 96, 98
98/2 = 49, so there are 49 multiples of 2
Multiples of 3: 3, 6, 9, ..., 99
99/3 = 33, so there are 33 multiples of 3
At this point we have counted some multiples TWICE. For example, we counted 6 TWICE, we counted 12 TWICE and so on.
In fact, we counted all multiples of 6 TWICE
Multiples of 6: 6, 12, 18..., 96
96/6 = 16, so there are 16 multiples of 6
So.....TOTAL multiples of 2 OR 3 = 49 + 33 - 16 = 66
There are 99 positive integers that are less than 100
So, the TOTAL number of those integers that are NEITHER multiples of 2 or 3 = 99 - 66 = 33
Answer: D
Cheers,
Brent
gmatclubot
Re: How many positive integers less than 100 are neither multiples of 2 or [#permalink]
18 Apr 2022, 13:27
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