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

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CEO
Joined: 21 Jan 2007
Posts: 2764
Location: New York City
Followers: 9

Kudos [?]: 348 [0], given: 4

What is the number of integers from 1 to 1000 (inclusive) [#permalink]  16 Nov 2007, 01:58
What is the number of integers from 1 to 1000 (inclusive) that are not divisible by 11 nor by 35?

A. 884
B. 999
C. 123
D. 124
E. 231
Manager
Joined: 25 Jul 2007
Posts: 108
Followers: 1

Kudos [?]: 14 [1] , given: 0

1
KUDOS

Total multiples of 35 between 1 & 1000 = 28 (35*28=980)
Total multiples of 11 between 1 & 1000 = 90 (90*11=990)
Total multiples of 11 and 35 between 1 & 1000 = 2 (35*11 = 385 & 770)

Therefore 28+90-2=116

1000-116 = 884.
Manager
Joined: 20 Sep 2006
Posts: 58
Followers: 1

Kudos [?]: 4 [0], given: 0

Agree. Ans is A).
Took me 3 mins to solve though
SVP
Joined: 28 Dec 2005
Posts: 1583
Followers: 2

Kudos [?]: 86 [0], given: 2

is there a shorter way to figure out the #s of multiples, especially for 35 ?
Director
Joined: 09 Aug 2006
Posts: 525
Followers: 2

Kudos [?]: 39 [0], given: 0

Re: 7.14 Counting [#permalink]  16 Nov 2007, 20:27
bmwhype2 wrote:
What is the number of integers from 1 to 1000 (inclusive) that are not divisible by 11 nor by 35?

A. 884
B. 999
C. 123
D. 124
E. 231

Yes A. Could solve in 1 min..

I went this way.. There are 9 multiples of 11 from 1 - 100 so from 1 -1000 they would be ~90.
There are 2 multiples of 35 in 1-100 hence from 1-1000, they will be ~20.. So total will be ~110.. Only A comes close .. I would have been screwed choices were closer ..
Manager
Joined: 25 Jul 2007
Posts: 108
Followers: 1

Kudos [?]: 14 [0], given: 0

pmenon wrote:
is there a shorter way to figure out the #s of multiples, especially for 35 ?

This is how i did it.

Find any easy-to-calculate multiple of 35 close to 1000.
e.g: 35 * 30 = 1050.

Work from there to get 980 = 35*28.

Hope this helps.
Director
Joined: 09 Aug 2006
Posts: 766
Followers: 1

Kudos [?]: 68 [0], given: 0

Re: 7.14 Counting [#permalink]  16 Nov 2007, 22:44
bmwhype2 wrote:
What is the number of integers from 1 to 1000 (inclusive) that are not divisible by 11 nor by 35?

A. 884
B. 999
C. 123
D. 124
E. 231

Total ints. = 1000

# of ints. divisible by 11 = 1000/11 = 90
# of ints. divisible by 35 = 1000/35 = 28
# of ints. divisible by both 11 & 35 = 1000/(LCM of 11, 35) = 1000/385 = 2

# of ints. not divisible by either = 1000 - (90+28) + 2 = 884
Manager
Joined: 03 Sep 2006
Posts: 233
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Kudos [?]: 5 [0], given: 0

Late, but A
The same method as jbs
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