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A Digital Root Problem (Posted on 2006-06-29) Difficulty: 2 of 5
The digital root of a number is obtained by summing its digits and then repeating the process (summing the sum's digits) until the answer is a single digit number. For example, the digital root of 7368 is 6.

Determine the digital root of (97240+38)8457

  Submitted by K Sengupta    
Rating: 4.0000 (2 votes)
Solution: (Hide)
The required digital root is 8.

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METHOD 1 (Submitted by Daniel):

The solution submitted by Daniel is given here which follows the hint.

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METHOD 2:

Digital Root of :
(97240 + 38)8457

= Digital Root of :
(28457 + 9* A Large Number)

= Digital Root of :
(82819) + 9

= Digital Root of :
((9-1)2819 + 9)

= Digital Root of :
( (9*(A large number) - 1) + 9)

= Digital Root of :
(9 - 1+ 9)

= 8

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METHOD 3:

97240 + 38
= 38 (Mod 9)
= 2 (Mod 9)

Accordingly:

(97240 + 38)8457
= 28457 (Mod 9)
= 82819(Mod 9)
=(-1)2819 (Mod 9)
= (-1) (Mod 9)
= 8 ( Mod 9)

Since, the remainder of the given number (97240 + 38)8457 upon division by 9 is 8, and 8 is not congruent to 0 Mod 9, it follows from Raman's Formula that the required digital root must be 8.

NOTE : Definitions of Mod n are given in this location as well as here .

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: very simplistic explanationK Sengupta2006-07-11 14:49:27
CreditsK Sengupta2006-07-11 14:00:38
Solutionvery simplistic explanationJohn2006-07-10 05:02:29
re: DifficultyDaniel2006-06-29 22:53:04
re: DifficultyRichard2006-06-29 19:37:36
DifficultySir Percivale2006-06-29 18:21:01
re: AnswerRichard2006-06-29 15:08:04
SolutionAnswerOld Original Oskar!2006-06-29 14:33:30
Solution SpoilerDaniel2006-06-29 11:48:24
HintDaniel2006-06-29 11:43:35
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