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# How many positive multiples of 6 that are less than 1000 are NOT multi

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How many positive multiples of 6 that are less than 1000 are NOT multi  [#permalink]

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Updated on: 27 Feb 2019, 05:29
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How many positive multiples of 6 that are less than 1000 are NOT multiples of 8?
(A) 121
(B) 124
(C) 125
(D) 148
(E) 166

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Originally posted by EncounterGMAT on 26 Feb 2019, 11:09.
Last edited by EncounterGMAT on 27 Feb 2019, 05:29, edited 1 time in total.
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Re: How many positive multiples of 6 that are less than 1000 are NOT multi  [#permalink]

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26 Feb 2019, 13:51
# +ve integers less than 1000 divided by 6 = 1000/6 -->166
# +ve integers less than 1000 divided by 24 = 1000/24 -->41 ( the numbers div by 24 , will also be div by 6 & 8.. as 24 is lcm of 6&8)
Hence, # positive multiples of 6 that are less than 1000 are NOT multiples of 8 = 166-41= 125
Ans C
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Re: How many positive multiples of 6 that are less than 1000 are NOT multi  [#permalink]

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27 Feb 2019, 05:29
u1983 wrote:
# +ve integers less than 1000 divided by 6 = 1000/6 -->166
# +ve integers less than 1000 divided by 24 = 1000/24 -->41 ( the numbers div by 24 , will also be div by 6 & 8.. as 24 is lcm of 6&8)
Hence, # positive multiples of 6 that are less than 1000 are NOT multiples of 8 = 166-41= 125
Ans C

1000/24= 41.667. So shouldn't the number be rounded off to 42?
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Re: How many positive multiples of 6 that are less than 1000 are NOT multi  [#permalink]

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27 Feb 2019, 08:24
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topper97 wrote:
u1983 wrote:
# +ve integers less than 1000 divided by 6 = 1000/6 -->166
# +ve integers less than 1000 divided by 24 = 1000/24 -->41 ( the numbers div by 24 , will also be div by 6 & 8.. as 24 is lcm of 6&8)
Hence, # positive multiples of 6 that are less than 1000 are NOT multiples of 8 = 166-41= 125
Ans C

1000/24= 41.667. So shouldn't the number be rounded off to 42?

Hello topper97 ... sry for the confusion.

We were trying to find how many +ve integers are there <1000 , those are divisible by 24.
To do that you can use 1000/24=41.667 ... then rounded up to nearest low integer.

Check this way .... if there are 42 integers those are div by 24, the 42nd one would be 42*24=1008 >1000

Hope this helps !!
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Re: How many positive multiples of 6 that are less than 1000 are NOT multi  [#permalink]

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27 Feb 2019, 09:09
u1983 got it! Thanks for the explanation.
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Re: How many positive multiples of 6 that are less than 1000 are NOT multi  [#permalink]

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27 Feb 2019, 09:36
topper97 wrote:
u1983 got it! Thanks for the explanation.

Hello topper97 ... No problem. I am glad it helped. !!
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Re: How many positive multiples of 6 that are less than 1000 are NOT multi  [#permalink]

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01 Mar 2019, 10:48
topper97 wrote:
How many positive multiples of 6 that are less than 1000 are NOT multiples of 8?
(A) 121
(B) 124
(C) 125
(D) 148
(E) 166

If a number is a multiple of 6 and it’s not a multiple of 8, then it’s not a multiple of 24 since 24 is the LCM of 6 and 8.

Let’s determine the number of multiples of 6 less than 1000:

(996 - 6)/6 + 1 = 166

Next we need to determine the number of multiples of 24 less than 1000:

(984 - 24)/24 + 1 = 41

Thus, the number of positive multiples of 6 that are less than 1000 and are NOT multiples of 8 is 166 - 41 = 125.

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Re: How many positive multiples of 6 that are less than 1000 are NOT multi   [#permalink] 01 Mar 2019, 10:48
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