On planet Jupiter the people use a certain number system to the base ‘n’ (n > 2), Jerk, a resident of the planet, one day received twice his daily wage because the digits of this wage, which was a 2 digit number, were reversed. If the value of ‘n’ is the least possible value there the decimal representation of the difference between Jerk’s correct wage for the day is
Options:  A) 8  B) 9  C) 10  D) 11  E) 12
Sol:   Let the base of the number system be n and the two digit number be ab   given 2(ab)n = (ba)n   ⇒⇒ nb + a = 2na + 2b   ⇒⇒ a(2n - 1) = b(n - 2)   ⇒a/b= n−2 /2n−1   Now the maximum possible value of a or b is (n - 1) (base n) for n = 3 we get   a/b=1/5 which is not possible as in base 3, 5 won't exist.   Similarly, for n = 4   but for n = 5   We get a/b=3/9 i.e.1/3   a = 1, b = 3 is the only number possible when n is the least possible.   The correct wage = (13)5=(8)10   The actual wage paid = (31)5=(16)10   So difference = 8   8nswer 8
<result>A</result>
On planet Jupiter the people use a certain number system to the base ‘n’ (n > 2), Jerk, a resident of the planet, one day received twice his daily wage because the digits of this wage, which was a 2 digit number, were reversed. If the value of ‘n’ is the least possible value there the decimal representation of the difference between Jerk’s correct wage for the day is