## How many positive integers less than 100 are neither multiples of 2 or 3.

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### How many positive integers less than 100 are neither multiples of 2 or 3.

by BTGmoderatorDC » Mon May 23, 2022 6:37 am

00:00

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B

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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

OA D

Source: GMAT Prep

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### Re: How many positive integers less than 100 are neither multiples of 2 or 3.

by [email protected] » Thu May 26, 2022 10:10 am
BTGmoderatorDC wrote:
Mon May 23, 2022 6:37 am
How many positive integers less than 100 are neither multiples of 2 or 3.

a)30
b)31
c)32
d)33
e)34

OA D

Source: GMAT Prep
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