Question

The sum of all natural numbers ${}^{\prime }{n}^{\prime }$ such that $100<n<200$ and H.C.F. $(91,n)>1$ is:

• A. $3203$
• B. $3221$
• C. $3121$
• D. $3303$

Answer 1

The correct option is C $3121$

Numbers between $100$ and $200$ which are divisible by $7$:
$105,112,\cdots ,196$.
Let their sum be $S_1$.
$\therefore S_1=\frac{14}{2}(105+196)=2107$

Numbers between $100$ and $200$ which are divisible by $13$:
$104,117,\cdots ,195$.
Let their sum be $S_2$.
$\therefore S_2=\frac{8}{2}(104+195)=1196$

Number between $100$ and $200$ which is divisible by $7$ and $13$ both =$182$
Hence, required sum=$2107+1196-182=3121$