Question

Find the number of integers between$100$ & $1000$ that are
i) divisible by $7$
ii) not divisible by $7$

Answer 1

i)

Next number after 100 which is divisible by 7 is 105 and biggest three digit number divisible by 7 is

1000÷7 has 6 as reminder

$\therefore$ 1000–6=994

994=7*142

105=7*15

Therefore between 100 and 1000 there will be

142–15=127 numbers divisible by 7 and considering 105 there are 128 such numbers.

ii)

There are total 889 numbers between 100 and 1000 out of which 128 numbers are divisible by 7

$\therefore$ Remaining numbers i.e. 899 - 128 = 771 are not divisible by 7.