Question

The number of numbers which are divisible by $7$ between $100$ and $1000$ is

• A. $7$
• B. $128$
• C. $132$
• D. $127$

Answer 1

The correct option is B $128$

numbers divisible by $7$ between $100$ and $1000$
So, $a=105,d=7,$
To find $T_n$, divide $1000$ by $7$ and note the remainder i.e., $6$
So the number divisible by $7$ and the greatest three digit no.less than $1000$ is $994$
i.e., $T_n=994$
But $T_n=a+(n-1)d$
So, $994=105+(n-1)7$
i.e., $127=n-1$
i.e., $n=128$