Question

The number $N=6{\log }_{10}2+{\log }_{10}31$ lies between two successive integers whose sum is equal to

• A. $5$
• B. $6$
• C. $7$
• D. $9$

Answer 1

The correct option is C $7$

$N=6{\log }_{10}2+{\log }_{10}31$
$\Rightarrow N={\log }_{10}64+{\log }_{10}31\Rightarrow N={\log }_{10}1984\Rightarrow {10}^N=1984\therefore 3<N<4$

Hence, the sum of successive integer is $3+4=7$