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# What is the number of integers from 1 to 1000 (inclusive)

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What is the number of integers from 1 to 1000 (inclusive) [#permalink]

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16 Jan 2012, 08:56
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What is the number of integers from 1 to 1000 (inclusive) that are divisible by neither 11 nor by 35?

A. 884
B. 890
C. 892
D. 910
E. 945
[Reveal] Spoiler: OA

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Last edited by Bunuel on 07 Jul 2013, 05:34, edited 1 time in total.
Edited the question.
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Re: what is teh number of integers from 1 to 1000 [#permalink]

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16 Jan 2012, 11:17
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manalq8 wrote:
What is the number of integers from 1 to 1000 (inclusive) that are divisible by neither 11 nor by 35?

884
890
892
910
945

what's the quickest way to solve this questions do you think?
I will provide the my approach and the OA once I see yours

thanks alot

# of multiples of 11 in the given range (last-first)/multiple+1=(990-11)/11+1=90 (check this: totally-basic-94862.html);
# of multiples of 35 in the given range (last-first)/multiple+1=(980-35)/35+1=28;
# of multiples of both 11 and 35 is 2 (11*35=385 and 770);

So, # of multiples of 11 or 35 in the given range is 90+28-2=116. Thus numbers which are not divisible by either of them is 1000-116=884.

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Re: what is teh number of integers from 1 to 1000 [#permalink]

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17 Jan 2012, 03:12
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manalq8 wrote:
What is the number of integers from 1 to 1000 (inclusive) that are divisible by neither 11 nor by 35?

884
890
892
910
945

what's the quickest way to solve this questions do you think?
I will provide the my approach and the OA once I see yours

thanks alot

Normally, I would use the method used by Bunuel. It's the most accurate. But if you are looking for a speedy solution, you can use another method which will sometimes give you an estimate. Looking at the options (most of them are spread out), I wont mind trying it. (Mind you, the method is accurate here since the numbers start from 1.)

In 1000 consecutive numbers, number of multiples of 11 = 1000/11 = 90 (Ignore decimals)
In 1000 consecutive numbers, number of multiples of 35 = 1000/35 = 28
Number of multiples of 11*35 i.e. 385 = 1000/385 = 2

Number of integers from 1 to 1000 that are divisible by neither 11 nor by 35 = 1000 - (90 + 28 - 2) {Using the concept of sets here) = 884

Think: Why did I say the method is approximate in some cases?
Think what happens if the given range is 11 to 1010 both inclusive (again 1000 numbers)
What is the number of multiples in this case?
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Re: what is teh number of integers from 1 to 1000 [#permalink]

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18 Jan 2012, 13:48
Thanks alot Bunuel!

Karishma, you said it accurate I think because if 1 is involved then it will yield more accurate results.
ok, given the range you gave me..
how can I use the method you demonistrated. should just say 1000/11 and 1000/35 and 1000/11*35? or 1010-11/11 and 1010-11/35 and 1010-11/35*11 and subtract the result from 1000?

question. the number 1000 you used in your method(when dividing by 11,35 and 11*35) refers to the number of elements in the given range or you the result you get when subtracting the smallest from the largest ?

thanks alot
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Re: What is the number of integers from 1 to 1000 (inclusive) [#permalink]

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10 Sep 2014, 15:50
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What is the number of integers from 1 to 1000 (inclusive) [#permalink]

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27 Jun 2015, 14:36
The method is approximate since the solution could be $$1$$ off, at a minimum, from your estimated solution. This occurs because the quotient is non-inclusive, none of the ends are unaccounted for. As well, another multiple of $$11$$ is added at $$100$$1, and therefore the answer will be $$+(10-1)$$ of a difference.
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16 Jul 2016, 03:04
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Re: What is the number of integers from 1 to 1000 (inclusive) [#permalink]

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16 Jul 2016, 04:22
manalq8 wrote:
What is the number of integers from 1 to 1000 (inclusive) that are divisible by neither 11 nor by 35?

A. 884
B. 890
C. 892
D. 910
E. 945

Number divisible by 11:-
1000/11= 90

numbers divisible by 35:-
1000/35= 28

Numbers divisible by both 11 and 35= 2

Total numbers divisible by both 11 and 28= 90+28-2= 116 (because we counted 2 in both 90 and 28)

Total numbers not divisible by 11 or 35= 1000-116= 884

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Re: What is the number of integers from 1 to 1000 (inclusive) [#permalink]

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29 Nov 2016, 19:03
Numbers divisible by 11: 1001/11 = 91
Numbers divisible by 35: 1001/35 = 28
Numbers divisible by 11x35: 1001/385 = 2

1001-(91+28)+2 = 884

A.
Re: What is the number of integers from 1 to 1000 (inclusive)   [#permalink] 29 Nov 2016, 19:03
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