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Q. A=8888^8888,B is the sum of the digit of A, C is the sum of the digit of B and so on….in this series there is a point where u will get sum of digits of X=X.find X ?
options — 1, 2, 7, 5, 6

[Wonder Boy]

Lets factorise 8888 to some smaller numbers.

So 8 + 8 + 8 + 8 = 32 ~ 5

Now as Digital Sum Rule of Multiplication says : The digital sum of the product of two numbers is equal to the digital sum of the product of the digital sums of the two numbers.

so digital sum of digits of 8888⁸⁸⁸⁸ = digital sum of 5⁸⁸⁸⁸

Now 5² = 25 ~ 7

so digital sum of 5⁸⁸⁸⁸ = digital sum of (5²)⁴⁴⁴⁴ = digital sum of 7⁴⁴⁴⁴

Now 7³ = 343 ~ 10 ~ 1 and 7⁴⁴⁴⁴= (7³)¹⁴⁸¹x7

so digital sum of 7⁴⁴⁴⁴ = digital sum of(7³)¹⁴⁸¹x digital sum of 7 = 1¹⁴⁸¹ x7 = 7 Ans

[Author]

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