Question

Find the digit sum (till you get a single digit number) of the smallest element of set P. The smallest element in set P can be represented as $\left(8^x\right)\left({25}^{300}\right)$, which consists of 604-609 digits, where x is a natural number.

• A. 9
• B. 8
• C. 1
• D. 11

Answer 1

The correct option is C 1

$2^{600}\times 5^{600}$ will have 601 digits (1 followed by 600 zeroes). To get the minimum, 604 digits we will have to increase the power of 2 such that we get a four digit number followed by 600 zeroes. The power should also be a multiple of 3 as $8=2^3.$ The smallest such power is $2^{12}=8^4$. Therefore, smallest element of set $P=8^{204}\times 5^{600}=\mathrm{4096000000.....600}zeroes(604$ digits$)$. The sum of the digits of $P$ min $=19=1.$