Question

N is a 1001 digit number consisting of 1001 sevens. What is the remainder when N is divided by 1001?

• A. 7
• B. 700
• C. 777
• D. None of these

Answer 1

The correct option is B 700

We have to find Rem (777777.... 1001 times)/(1001)
Now, we know that $1001=7\times 11\times 13$
Clearly, 7777.... 1001 times is divisible by 7. now checking for 11
and 13, we get the form 11k+1 = 13l+9 => 11k - 13l = 8
for k =9 and l = 7, the above equation satisfies, hence the remainder when 777777......is divided by 1001 is 7*(11k+1) => 7*(100) = 700