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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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9
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45% (medium)

Question Stats:

64% (01:37) correct 36% (01:54) wrong based on 650 sessions

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

A. 599
B. 600
C. 601
D. 602
E. 603
Math Expert
Joined: 02 Sep 2009
Posts: 58402
Re: GMAT Club - [t]m16#11[/t]  [#permalink]

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12 Jun 2010, 12:54
5
5
gmatcracker2010 wrote:
How many three-digit integers are not divisible by 3 ?

* 599
* 600
* 601
* 602
* 603

OA is

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
5
1
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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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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23 Aug 2016, 21:32
1
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
1
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
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Re: How many three-digit integers are not divisible by 3 ?  [#permalink]

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16 Mar 2018, 04:34
Bunuel wrote:
gmatcracker2010 wrote:
How many three-digit integers are not divisible by 3 ?

* 599
* 600
* 601
* 602
* 603

OA is

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

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

Hope it helps.

Total 3 digit numbers: 999−100+1=900999−100+1=900.
How to calculate total 3digit numbers?
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Re: How many three-digit integers are not divisible by 3 ?  [#permalink]

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16 Mar 2018, 04:49
1
Priyansha7 wrote:
Total 3 digit numbers: 999−100+1 = 900.
How to calculate total 3digit numbers?

Hey Priyansha7 ,

Total 3 digit numbers are all the numbers from 100 to 999.

So, Either I can say find out the numbers from 101 to 999 and add 1 to it for the number 100, which will be equal to 999-100 + 1 = 900

Or I can say Subtract first 99 numbers from 999 numbers = 999 - 99 = 900

Does that make sense?
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How many three-digit integers are not divisible by 3 ?  [#permalink]

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18 Mar 2018, 16:30
gmatcracker2010 wrote:
How many three-digit integers are not divisible by 3 ?

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

Three-digit numbers range from 100 to 999

How many 3-digit numbers total?
Inclusive: (Greatest-Least) + 1
(999 - 100) = 899 + 1 = 900 numbers altogether

1) Find a pattern - divisible by 3? (digits must sum to 3 or a multiple of 3)
100: no
101: no
102: yes
103: no
104: no
105: yes

2 out of 3, $$\frac{2}{3}$$, are NOT divisible by 3

$$\frac{2}{3}*900 = 600$$

2) Use evenly spaced set's properties* to find how many numbers ARE divisible by 3, i.e. find how many are multiples of 3

Subtract those multiples of 3 from the total of 3-digit numbers

First and last multiples of 3 in this range?

The first multiple of 3 is 102
The last multiple of 3 is 999

Number of terms (multiples of 3) =

$$\frac{(Last Term-FirstTerm)}{Increment} + 1$$

$$(\frac{999-102}{3}+1)=(\frac{897}{3}+1)=(299+1)=300$$

There are 900 numbers from 100 to 999

300 ARE divisible by 3

(900-300) = 600 are NOT divisible by 3

*
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How many three-digit integers are not divisible by 3 ?   [#permalink] 18 Mar 2018, 16:30
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