A three digit non zero number 39 abc 39 in base 5 when converted to base 7 becomes 39 cba 39 Wh...........

Quantitative Aptitude ( CCS) Number System

A three digit non-zero number 'abc' in base 5, when converted to base 7, becomes 'cba'. Which of the following is necessarily true?

a must be 2

c must be 2

b must be 0

None

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Explanation:

Given (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.
Hence, option 3 is the correct answer.