xyz+AB =CDEF and xyz-AB=BGA

• Ans:The value C will take is '1' since max XYZ is 999 and max AB is 99.
  X has to take a value '9' only then we can carry over '1'.
  Looking at XYZ - AB = BGA there are two important things:
  Z - B = A and A > Y so, X - 1 = B. Also 1Y - A = G
  This means B = '8' since we know X is '9'.
  Now looking at XYZ + AB = CDEF
  Since we know X is '9' we know C is '1' and D can only be '0'.
  So now '9'YZ + A'8' = '1''0'EF and
  '9'YZ - A'8' = '8'GA. Digits remaining 2,3,4,5,6,7
  '1'Y - A = G and '1'Z - '8' = A
  Simplest way is trial and error
  Simple assumption is Z = 5 which gives A = 15 - 8 = 7
  '9'Y'5' - 78 = '8'G'7' so 945 - 78 = 867
  945 + 78 = 1023
• 10 years agoHelpfull: Yes(14) No(0)
• clearly explain d qn..
  
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• Q.XYZ + AB = CDEF
  XYZ - AB = BGA
  All the letters have distinct values. find X, Y & Z?
• 10 years agoHelpfull: Yes(3) No(0)
• xyz+AB=CDEF (1)
  xyz-AB=BGA (2)
  from (2) AB=xyz-BGA (3)
  sub (3) in (1)
  xyz+xyz-BGA=CDEF
  2xyz=CDEF+BGA
  xyz=(CDEF+BGA)/2
• 10 years agoHelpfull: Yes(2) No(0)
• xyz+AB=CDEF.....1
  xyz-AB=BGA......2
  from 1 and 2 AB will get cancelled...Therefore 2xyz=ABCDEFG
  ans=ABCDEFG/2
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• anyone plz explain this
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