Question

An n-digit number x has the following property: if the last digit of x is moved to the front, the
result is 2x. Find the smallest possible value of n.​

Answer 1

Answer:PRMO

Step-by-step explanation:

You are from which ca cmpus of naryana ,

Answer 2

18 is your answer mate

let be the last digit of x then X equal to 10 + D

after moving the last digit to front then the number becomes

10^n-1 d+c

• according to question
• 10^n-1 d+c=2(10c+d) which is also equal to (10^n-1 minus 2)d=19c
• computing 10power k modulo 19 for k equal to 1,2,3........we get 10,5,12,6,3,11,15,17,18,9,14,7,13,16,8,4,2
• hence the smallest possible value of n-1 is 17
• which implies it to be c=17 digit number

from (10^n-1 minus 2)d=19c

so d=2 then n=18 digit number

hope you understand mate

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