When a certain number 'x' is multiplied bt 18, the product 'y' has all digits as 4s. what is the minimum number of digits 'x' can have?
a) 8
b) 9
c) 12
d) 18

• 18=9*2
  444......4/9*2 = 22222....2/9
  to be completely divisible sum of all 2's should be a multiple of 9(divisibility test for 9)
  so it should have 9 digit (2+2+2+2+2+2+2+2+2=18)
  answer is --->>> b) 9
• 9 years agoHelpfull: Yes(36) No(16)
• Factors of 18 is 3*3*2. Therefore the solution must be a multiple of 9 which can be achieved by taking 9 times 4 as part of the question given.
  So
  X*18=444444444
  Therefore x =24691358. That's a 8 digit number. So And is (a)
• 9 years agoHelpfull: Yes(18) No(5)
• @saurav kumar i think u are right ....
  
  Question says
  
  X*18=Y....
  
  and Y=4444.....4
  so lets figure value for x...
  
  Going back to our equation...
  
  X=Y/18
  or, X=4444...4/18
  
  now because 18 has 9 in it... so y will divisible by 18 or just 9 if there 9 fours...
  
  now
  444444444/18=24691358...this is x
  
  hence now count the minimum digits...... yes its 8
• 9 years agoHelpfull: Yes(6) No(0)
• Ans is 8,that explanation is correct,y will be 9(but not asked)
• 9 years agoHelpfull: Yes(1) No(0)
• Can anyone xpln y it is nt 8
• 9 years agoHelpfull: Yes(0) No(0)
• option (b)
• 9 years agoHelpfull: Yes(0) No(0)
• in this question we are basically checking the product ''y'' divisibility by 9
  9X2=18 , 9= chain of digits 4, since any number divisible by 9 its digital sum should be divisible by 9 therefore 4+4+4+4+4+4+4+4+4=36= 3+6=9 . therefore b is the answer
• 7 years agoHelpfull: Yes(0) No(0)
• @Prashant has given incomplete solution.
  Here it is,
  after doing this
  
  [18=9*2
  444......4/9*2 = 22222....2/9
  to be completely divisible sum of all 2's should be a multiple of 9(divisibility test for 9)
  so it should have 9 digit (2+2+2+2+2+2+2+2+2=18)]
  
  Now x= (2+2+2+2+2+2+2+2+2)/9
  
  x=24691358 So answer is 8 digits.
• 2 years agoHelpfull: Yes(0) No(0)