Let ABC be the largest 3 digit perfect square in base 6 (A, B, C <= 5) => in base 10 ABC will be 36A + 6B + C and this number is a perfect square. Since 5*(36 + 6 + 1) = 215 => 36A + 6B + C = 14^2 = 196 => ABC = 524.

Now, 524 is written as a 2 digit number CD in base b => b*C + D = 524 where C, D < b and C is a positive integer => b ranges from 23 to 524 => x = 502 = 1315 in base 7.

The properties (odd/even/prime/perfect square) of a number N in base b is same as that of decimal conversion of N => x is even in base 7 also.

=> Choice (4) is the right answer.