Question

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

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

Answer 1

Answer: (B)

$S_A$ = sum of numbers between 100 & 200 which are divisible by 7.
$\Rightarrow S_A=105+112+....+196$
$S_A=\frac{14}{2}[105+196]=2107$
$S_B$ = Sum of numbers between 100 & 200 which are divisible by 13.
$S_B=104+117+...+195=\frac{8}{2}[104+195]=1196$
$S_c$ = Sum of numbers between 100 & 200 which are divisible by both 7 & 13.
$S_c$ = 182
$\Rightarrow$ H.C.F. (91, n) > 1 = $S_A+S_B-S_c=3121$