Question

If $N={70}^{2730}+{30}^{2780}$ is divisible by ${10}^x$ (x is a natural number), find the rightmost non-zero integer in the remainder when N is divided by ${10}^{x+1}$ (if x is maximum).

• A. 7
• B. 1
• C. 9
• D. 0

Answer 1

The correct option is C

9

The question is based on the last non-zero digit (i.e. remainder when the number is divided by 10), as when x is maximum, ${10}^x$ will cancel out all the zeroes in the end.

It now becomes a question based on the rightmost non-zero integer in $7^{2730}$ (${30}^{2780}$ will end with more zeroes).

$7^{2730}⟹2730=4K+2$

Thus, the rightmost non-zero integer is 9.