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

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Director
Joined: 09 Aug 2006
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What is the number of integers from 1 to 1000 inclusive that [#permalink]  17 Jul 2007, 14:34
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What is the number of integers from 1 to 1000 inclusive that are not divisible by 11 nor by 35?

a) 884
b) 890
c) 892
d) 910
e) 945

Senior Manager
Joined: 03 Jun 2007
Posts: 384
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GK_Gmat wrote:
dahcrap wrote:
I got A

How?

Lets see.

Number of numbers between 1 and 1000 divisible by 11 is 90. Similarly there are 28 numbers divisible by 35. Now remember to consider numbers that are divisible by both 11 and 35.There are 2 such numbers. So total is 1000 - 90 - 28 + 2 = 884
Current Student
Joined: 28 Dec 2004
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Location: New York City
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how do you figure out in a very timely fashion the numbers that are both divisible by 11 and 35??
Intern
Joined: 14 Jul 2007
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The best and easiest way to figure out the numbers divisible by 11 and 35 is to split it into its prime factors

Prime Factors of 11 = 11
Prime Factors of 35 = 7 and 5

Since there is no overlap, the Least Common Multiple is 11 *35 = 385

Now there are 2 such multiples of 385 below 1000 (i.e 385 and 770)

The rest of the reasoning is the same as that provided earlier
Director
Joined: 08 Jun 2007
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Can some still provide a better way . I am still confused.
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