Find the digit sum (till you get a single digit number) of the smallest element

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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

(8^{x}) (25^{300})

, which consists of 604-609 digits, where x is a natural number.

Answer: Option C
:
C
option (c)

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 = 8204 \times 5^{600} = 4096000000 (604

digits

)

. The sum of the digits of

P

min

= 19 = 1.

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