A three digit non-zero number 'abc' in base 5, when converted to base 7, becomes 'cba'. Which of the following is necessarily true? Choose the correct option
A) a must be 2
B) c must be 2
C) b must be 0
D) None
E) Cannot be determined
Sol:   Given (abc)5=(cba)7(abc)5=(cba)7   or 25a + 5b + c = 49c + 7b + a   or 24a = 2b + 48c   or 12a = b + 24c   as abc is a 3 digit number in base 5, the possible values for a, b and c are 0, 1, 2, 3, 4 only   The possible solutions of the above equation are:   (a, b, c) = (2, 0, 1) and (4, 0, 2) only   a can take value = 2 or 4   b can take value = 0 only   c can take value = 1 or 2 only.   So correct option c.   Answer b must be 0
<result>C</result>
A three digit non-zero number 'abc' in base 5, when converted to base 7, becomes 'cba'. Which of the following is necessarily true?