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# How many three-digit integers are not divisible by 3 ? 599

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How many three-digit integers are not divisible by 3 ? 599 [#permalink]  04 Aug 2008, 09:46
How many three-digit integers are not divisible by 3 ?
599
600
601
602
603
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Re: m16 nO. 11 [#permalink]  04 Aug 2008, 09:56
x97agarwal wrote:
How many three-digit integers are not divisible by 3 ?
599
600
601
602
603

three digit integers divisible by 3 = 999/3 = 333
three digit integers not divisible by 3 = 999-333=666

Am I missing something
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Re: m16 nO. 11 [#permalink]  04 Aug 2008, 09:58
x97agarwal wrote:
How many three-digit integers are not divisible by 3 ?
599
600
601
602
603

I get B.

Number of 3-digit integers:
999-100 + 1 = 900

Number of 3 digit multiples of 3:
3*n where 34 <= n <= 333 is a 3-digit integer divisible by 3.

333-34 + 1 = 300

900 - 300 = 600
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Re: m16 nO. 11 [#permalink]  04 Aug 2008, 10:01
x2suresh,

You're counting single and double-digit numbers as well with the 999 - (999 / 3) method

You want to find the largest 2-digit number that is divisible by 3, which is 99 and then the largest 3-digit number divisible by 3 which is 999.

999 - 99 = 900

900 / 3 = 300

Now how many 3 digit numbers are there anyway?

there should be 900. [999 - 99 = 900]

So 900 - 300 = the answer of 600.

x2suresh wrote:
x97agarwal wrote:
How many three-digit integers are not divisible by 3 ?
599
600
601
602
603

three digit integers divisible by 3 = 999/3 = 333
three digit integers not divisible by 3 = 999-333=666

Am I missing something

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J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a.

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Last edited by jallenmorris on 04 Aug 2008, 10:05, edited 2 times in total.
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Re: m16 nO. 11 [#permalink]  04 Aug 2008, 10:15
jallenmorris wrote:
x2suresh,

You're counting single and double-digit numbers as well with the 999 - (999 / 3) method

You want to find the largest 2-digit number that is divisible by 3, which is 99 and then the largest 3-digit number divisible by 3 which is 999.

999 - 99 = 900

900 / 3 = 300

Now how many 3 digit numbers are there anyway?

there should be 900. [999 - 99 = 900]

So 900 - 300 = the answer of 600.

x2suresh wrote:
x97agarwal wrote:
How many three-digit integers are not divisible by 3 ?
599
600
601
602
603

three digit integers divisible by 3 = 999/3 = 333
three digit integers not divisible by 3 = 999-333=666

Am I missing something

OOPS thanks buddy.
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Re: m16 nO. 11 [#permalink]  04 Aug 2008, 10:26
x97agarwal wrote:
How many three-digit integers are not divisible by 3 ?
599
600
601
602
603

100 to 1000 excluding 1000 are 3 digit numbers

900 = total 3 digit numbers
one third of 900=300 are divisible by 3 hence 600 numbers are not div by 3

IMO B
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Re: m16 nO. 11 [#permalink]  05 Aug 2008, 01:00
x97agarwal wrote:
How many three-digit integers are not divisible by 3 ?
599
600
601
602
603

There are 900 three digit numbers ranging from 100 to 999. So numbers not divisible by 3 = 2/3 (900) = 600
Re: m16 nO. 11   [#permalink] 05 Aug 2008, 01:00
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