Digits of a four digit numbers are in AP, not necessarily in the same order. Arithmetic mean of any two digits of the number is an integer. How many such numbers are possible?

• 90
  1)abcd are even, 42 possibilities
  2)abcd are odd, 48 possibilities
  total 90 possibilities
• 11 years agoHelpfull: Yes(2) No(0)
• As the arithmetic mean of any two integers is an integer
  
  =>
  1) a,b,c,d are equal or
  2) a,b,c,d are even and unequal
  3) a,b,c,d are odd and unequal
  
  1) If all are equal, 9 possibilities
  2) If all are even , 1 possibility
  3) If all are odd , 2 possibility
  
  => Total possibilities = 12
• 11 years agoHelpfull: Yes(0) No(2)
• bt options are
  A.84
  B.96
  C.90
  D.70
• 11 years agoHelpfull: Yes(0) No(0)
• If order is not necessary
  Then total number of possibilities is
  
  90 as explained by Shakti Gupta
  + 9 if all digits are equal
  
  => 90+9 = 99
• 11 years agoHelpfull: Yes(0) No(0)