Integers

IMO A.

IMO A but dont know how,

according to my calculation answer should be 880 but there is no such option mentioned in options. The closest answer choice is A

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

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

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