when we perform a digit slide on a number we move its units digit to the front of the number.for eg:the result of a digit slide on 6471 is 1647...let z be the samllest positive integer with 5 as its units digit such that the result of a digit slide on the number equals 4 times the number...how many digits will z have??

• ......5*4 = 20
  ......05*4 = 20
  ......205*4 = 820
  .....8205*4 = 32820
  ....28205*4 = 112820
  ....128205*4 = 512820
• 10 years agoHelpfull: Yes(17) No(2)
• 128205*4 = 512820
  
  so Z will have 6 digits.
• 12 years agoHelpfull: Yes(9) No(13)
• Equation is :-
  
  4(10X+4)=4*10^k+x.
  
  Solve for X. After trying different values of k finally k=5 satisfies the solution.Hence the number is 102564
• 11 years agoHelpfull: Yes(2) No(8)
• Let the result of a ‘digit slide’ on z be x.
  Given that unit digit of z is 5.
  So z will be of the form:
  z = *********5, number of stars in z do not indicate the number of digits in z
  
  * * * * * * * * * 5
  Also, given that x is 4 times of z so the unit digit of x will be 0
  Hence x will be of the form:
  x = *********0, number of stars in x do not indicate the number of digits in x
  
  Since x is a ‘digit slide’ of z, the unit place digit of z is the leading digit of x.
  Hence x will be of the form:
  x = 5********0
  
  Notice that x is a ‘digit slide’ of z, so the unit place digit of x will be the ten place digit of z.
  So now z is of the form:
  z = **********05
  
  One important point: Since x is 4 times of z and the leading digit in x is 5. This implies that the leading digit in z must have been 1. This is because, after multiplying z by 4 we are getting just 5 at the leading position which has been a result of multiplication by 4 and adding the carry 1 from the previous one.
  So now z is of the form: 1 * * * * * * * 0 5
  
  Again, x is 4 times that of z and 4 times of z produces a result whose ten place digit is 2, so x will have 2 as ten place digit.
  x = 5*******20
  So now x is of the form: 5 1 * * * * * * 2 0
  
  Ten place digit of x will be hundred place digit of z
  So now z is of the form:
  z = 1 * * * * * * 2 0 5
  
  4 times of z now gives hundred place digit as 8.
  So now x is of the form: 5 1 * * * * * 8 2 0
  
  Hundred place digit of x will be thousand place digit of z
  So now z is of the form: 1 * * * * * 8 2 0 5
  
  4 times of z now gives thousand place digit as 2.
  So now x is of the form: 5 1 * * * * 2 8 2 0
  
  Thousand place digit of x will be ten thousand’s place digit.
  So now z is of the form: 1 * * * * 2 8 2 0 5
  
  At this stage z is 128205 and x is 512820.
  Here x is 4 times of z.
  If we proceed further this way, we might get another such number but our aim was to find first such number and that number is 128205 which is a 6 digit number
• 8 years agoHelpfull: Yes(2) No(0)
• Please explai amit....
• 10 years agoHelpfull: Yes(0) No(1)