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# How many three-digit integers are not divisible by 3 ?

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Manager
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How many three-digit integers are not divisible by 3 ? [#permalink]  12 Jun 2010, 11:02
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Question Stats:

63% (02:10) correct 37% (01:16) wrong based on 231 sessions
How many three-digit integers are not divisible by 3 ?

A. 599
B. 600
C. 601
D. 602
E. 603
[Reveal] Spoiler: OA
Math Expert
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Re: GMAT Club - [t]m16#11[/t] [#permalink]  12 Jun 2010, 11:54
3
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Expert's post
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gmatcracker2010 wrote:
How many three-digit integers are not divisible by 3 ?

* 599
* 600
* 601
* 602
* 603

OA is
[Reveal] Spoiler:
b

Total 3 digit numbers: $$999-100+1=900$$.
Multiples of 3 in the range 100-999: $$\frac{999-102}{3}+1=300$$ (check this: totally-basic-94862.html#p730075).

{Total} - {# multiples of 3} = {# of not multiples of 3} --> $$900-300=600$$.

Hope it helps.
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Re: How many three-digit integers are not divisible by 3 ? [#permalink]  20 Dec 2012, 21:10
2
KUDOS
What are our three-digit numbers?
$$100$$ to $$999$$

How many numbers from 1 to 999 are divisible by 3?
$$\frac{999}{3}=333$$
999-333 = 666 numbers NOT divisible by 3

How many numbers from 1 to 99 are divisible by 3?
$$\frac{99}{3}=33$$
99-33 = 66 numbers NOT divisible by 3

$$666-66=600$$ numbers are NOT divisible by 3 from 100 to 999

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Re: How many three-digit integers are not divisible by 3 ? [#permalink]  09 Jul 2014, 06:07
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Re: How many three-digit integers are not divisible by 3 ? [#permalink]  24 Jun 2015, 08:01
1
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We can probably tag Sequence (Arithmetic Sequence) also in this.
gmatcracker2010 wrote:
How many three-digit integers are not divisible by 3 ?

A. 599
B. 600
C. 601
D. 602
E. 603

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Re: How many three-digit integers are not divisible by 3 ? [#permalink]  24 Jun 2015, 10:48
Expert's post
Hi All,

While the original post goes back about 5 years (so a question such as this could very well have been edited/updated during that time), the 'intent' of the question is to ask about POSITIVE 3-digit integers (and not all 3-digit integers, which would include negative integers).

GMAT assassins aren't born, they're made,
Rich
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Re: How many three-digit integers are not divisible by 3 ?   [#permalink] 24 Jun 2015, 10:48
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