KVPY Sample Paper KVPY Stream-SX Model Paper-31

Sum of the natural number between 100 and 200 whose HCF with 91 should be more than 1:

A) 1121

B) 3210

C) 3121

D) 1520

Correct Answer: C

Solution :

Natural numbers between 100 and 200.

101, 102, .... 199 Either divide by 7 or divide by 13.

(sum of numbers (divide by 7) + (sum of number divide by 13) - (sum of number of divide by 91)

\[\sum\limits_{r=1}^{14}{(98+7r)}+\sum\limits_{r=1}^{8}{(91+13r)}-(182)\]

\[=\left( 98\times 14+7.\frac{14\times 15}{2} \right)+\left( (91\times 8)+13\times \frac{8\times 9}{2} \right)-182\]

\[=1372+735+728+468-182=3121.\]