NMTC-2014 Bhaskara.

Number Theory Level 3

Let there be a number of five digits "N". 1 is added at the end of N to create a new number M. 1 is added before N to create a number O. If M=3*O ,Find the digital root of N.

Note- Digital root indicates digital sum operation repeated till there is a single digit answer obtained


The answer is 8.

Krishna Ar by Krishna Ar , 21, India

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2 solutions

Kshitij Alwadhi
Feb 20, 2016

Let N = abcde = x ;

N1 = M ;

1N = O ;

M= 10x + 1

O= 100000 + x

A.T.Q.

3*O = M

300000 + 3x = 10x + 1

299999 = 7x

x = 42857

Digital root = 4+2+8+5+7 = 2+6 = 8

2 Helpful 0 Interesting 1 Brilliant 0 Confused

Why have you taken N = 10 x N=10x in first line and written O = 100000 + x O=100000+x in the fifth line ?? I think O should be 1 ( 10 x ) 1(10x) . Please correct me . I think it should only me N = x N=x in the first line.

Chirayu Bhardwaj - 4 years, 9 months ago
Ankit Kumar Jain
Mar 12, 2015

The number is 42857

142857 × 3 = 428571 142857\times3 = 428571

1 Helpful 0 Interesting 0 Brilliant 0 Confused

But the answer is 8...? How?

Anshuman Singh Bais - 5 years, 11 months ago

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The number is 42857 42857 .

But the question asks for digital root i . e sum of digits till you reach a single digit, so digital root would be 4 + 2 + 8 + 5 + 7 = 26 4 + 2 + 8 + 5 + 7 = 26 , further 2 + 6 = 8 2 + 6 = 8 .

Ankit Kumar Jain - 5 years, 11 months ago

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