A three digit non-zero number 'abc' in base 5, when converted to base 7, becomes 'cba'. Which of the following is necessarily true?
option
1. a must be 2
2. c must be 2
3. b must be 0
4. None of these

• (abc) in base 5 = (cba) in base 7
  25a+5b+c= 49c+7b+a
  12a-b= 24c
  for this equation to satisfy,
  for 1st option when a is 2, this will not satisfy the question's condition
  but 2nd option satisfy the given condition as follows
  when c =2,a=4,b=0 . so no in base 5 is 402, now we covert it into base 7 , it will be equal to 204...So the correct answer is c must be 2
• 11 years agoHelpfull: Yes(3) No(0)
• only 3 statement true
  according to question:
  25a+5b+c=49c+7b+a
  48c+2b-24a=0
  it is possible when
  b=0 and c=2a
  so c may be 2 or 4 and a may be 1 or 2
• 11 years agoHelpfull: Yes(1) No(2)
• 3. b must be 0.
  
  As per given statement
  25a+5b+c=49c+7b+a
  48c+2b-24a=0
  b=12(a-2c)
  b can not be more than 4.
  so b must be zero only.
  a and c can have different values satisfying condition ,a-2c=0 or a=2c
  
• 11 years agoHelpfull: Yes(1) No(2)
• 1 and 3 must be true..
• 11 years agoHelpfull: Yes(0) No(3)