What is the number of integers from 1 to 1000 (inclusive) that are not divisible by 11 nor by 35?
884
890
892
910
945
884
890
892
910
945
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Integers
Source: Beat The GMAT — Problem Solving |
IMO A
I used approximation
Total number of integers between 1 and 1000 inclusive = 1000-1+1=1000
1. Find the number of integers divisible by 11 and 35
# of integers divisible by 11 = 1000/11 = 91 approx
# of integers divisible by 35 = 1000/35 = 29 approx
Total number of integers divisible by 11 and 35 = 91+29 = 120
2. The number of integers "not" divisible by 11 & 35 = 1000-120 = 880 approx
The "1000" used in 1 & 2 is the total number of integers between 1&1000 inclusive.
The answer choice closest to this option is A
I used approximation
Total number of integers between 1 and 1000 inclusive = 1000-1+1=1000
1. Find the number of integers divisible by 11 and 35
# of integers divisible by 11 = 1000/11 = 91 approx
# of integers divisible by 35 = 1000/35 = 29 approx
Total number of integers divisible by 11 and 35 = 91+29 = 120
2. The number of integers "not" divisible by 11 & 35 = 1000-120 = 880 approx
The "1000" used in 1 & 2 is the total number of integers between 1&1000 inclusive.
The answer choice closest to this option is A
Total numbers = 1000.
numbers divisible by 11 = 90 (last multiple is 990). ==> 910 numbers left.
nubers divisible by 5 are 200. => of these 200 numbrs divisible by 7 are 28 (28 * 7 = 196). So numbers divisible by 35 are 28.
Numbrs left = 910 - 28 = 882.
But, in those 28, we have 385 and 770 which are multiple of 11 aswell. so total number = 884.
Thanks,
Anil
numbers divisible by 11 = 90 (last multiple is 990). ==> 910 numbers left.
nubers divisible by 5 are 200. => of these 200 numbrs divisible by 7 are 28 (28 * 7 = 196). So numbers divisible by 35 are 28.
Numbrs left = 910 - 28 = 882.
But, in those 28, we have 385 and 770 which are multiple of 11 aswell. so total number = 884.
Thanks,
Anil
Total numbers = 1000.
numbers divisible by 11 = 90 (last multiple is 990). ==> 910 numbers left.
nubers divisible by 5 are 200. => of these 200 numbrs divisible by 7 are 28 (28 * 7 = 196). So numbers divisible by 35 are 28.
Numbrs left = 910 - 28 = 882.
But, in those 28, we have 385 and 770 which are multiple of 11 aswell. so total number = 884.
Thanks,
Anil
numbers divisible by 11 = 90 (last multiple is 990). ==> 910 numbers left.
nubers divisible by 5 are 200. => of these 200 numbrs divisible by 7 are 28 (28 * 7 = 196). So numbers divisible by 35 are 28.
Numbrs left = 910 - 28 = 882.
But, in those 28, we have 385 and 770 which are multiple of 11 aswell. so total number = 884.
Thanks,
Anil
