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

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Manager
Joined: 13 May 2010
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How many three-digit integers are not divisible by 3 ? [#permalink]

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12 Jun 2010, 12:02
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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
Joined: 02 Sep 2009
Posts: 39744
Re: GMAT Club - [t]m16#11[/t] [#permalink]

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12 Jun 2010, 12:54
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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]

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20 Dec 2012, 22:10
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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]

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09 Jul 2014, 07:07
Hello from the GMAT Club BumpBot!

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Re: How many three-digit integers are not divisible by 3 ? [#permalink]

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24 Jun 2015, 09:01
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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]

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24 Jun 2015, 11:48
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).

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Re: How many three-digit integers are not divisible by 3 ? [#permalink]

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10 Aug 2016, 00:10
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: How many three-digit integers are not divisible by 3 ? [#permalink]

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23 Aug 2016, 21:32
gmatcracker2010 wrote:
How many three-digit integers are not divisible by 3 ?

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

Total Single digit No. = 9 (1 to 9)
Total Two digit No. = 90 (10 to 99)
Total Single digit No. = 900 (100 to 999)

Total No. divisible by 3 from 1 through 999 = 999/3 = 333
Total No. divisible by 3 from 1 through 99 = 99/3 = 33

Total No. divisible by 3 from 100 through 999 = 333-33 = 300

So not divisible by 3 = 900-300 = 600

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Re: How many three-digit integers are not divisible by 3 ? [#permalink]

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25 Aug 2016, 09:59
Here Number of terms => 999-100+1=> 900
Terms divisible by 3 => 999-102/3 +1 =? 333-34 +1=> 300

Terms not divisible by 3 => 900-300 => 600

NOTE=> number of terms divisible by 3 + number of not divisible by 3 = total terms

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Re: How many three-digit integers are not divisible by 3 ? [#permalink]

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17 Apr 2017, 15:45
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gmatcracker2010 wrote:
How many three-digit integers are not divisible by 3 ?

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

first, let's find how many ARE divisible...
102 is the minimum one - it's the 34th multiple of 3.
999 is the maximum one - it's the 333 multiple of 3.
333-34 +1 (inclusive counting) = 300 numbers are divisible by 3.
now...we have 999 total numbers. we exclude the non 3 digit ones (from 1 to 99)
999-99=900
900-300=600
Re: How many three-digit integers are not divisible by 3 ?   [#permalink] 17 Apr 2017, 15:45
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