Question

How many three digit numbers are divisible by $5$?

• A. $180$
• B. $190$
• C. $150$
• D. $170$

Answer 1

The correct option is A $180$

The smallest and the largest numbers of three digits, which are divisible by 5 are 100 and 995 respectively,

So, the sequence of three digits numbers which are divisible by 5 is $100,105,110,...,995$.

It is an AP with first term $a=100$ and common difference $d=5$.
Let there be $n$ terms in this sequence. Then,
$a_n=995\Rightarrow a+(n-1)d$

$995=100+(n-1)\times 5$
$\Rightarrow n-1=179$

$\Rightarrow n=180$