Question

The sum of the digits of the number ${10}^n-1$ is $3798$. The value of $n$ is

• A. $337$
• B. $422$
• C. $335$
• D. $3375$

Answer 1

The correct option is B $422$

${10}^n-1$

for $n=1$

${10}^1-1=10-1=9=9\times 1$

for $n=2$

${10}^2-1=100-1=99\to 9+9=9\times 2$

Same for $n=3$

Therefore the sum of the digits will be $9$ times the number of $9^{\prime }ns.$

i.e $9n=3798$

Thus, the number of nines is

$\frac{3798}{9}=422$

Thus, option B is the correct answer.