How many integers between 1000 and 9999 inclusive are divisi

How many integers between 1000 and 9999 (inclusive) are divisible by 5 but not 7?

9999/5=1999.8

that means there are 1999 numbers divisible by 5 which are less than 9999

1000/5=200

that means there are 200 numbers divisible by 5 which are less than 1000 inclusive 1000.

so integers between 1000 and 9999 (inclusive) are=1999-200+1=1800

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any multiple of 5*7 that is of 35 will be divisible by both 5 and 7

using above method we get there are total 257 integers between 1000 and 9999 (inclusive) divisible by 5 and 7 both

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now to find integers between 1000 and 9999 (inclusive) which are divisible by 5 but not 7, we subtract 257 from 1800

1800-257=1543.

Hence final answer is 1543.