The question asked is the minimum number of bits required to REPRESENT Z and NOT minimum number of bits to calculate Z. Strictly speaking this question is all about the HARDWARE implementation of sign magnitude addition and subtraction of 2 numbers, X and Y and not just paper and pencil arithmetic, a frequently asked question in Research Programme Interviews in COA. This is explained in detail on page 417, chap.10, Digital Logic and Design by Moris Mano, 13th impression, 2011. Exactly 8 conditions arise when X and Y are added or subtracted .i.e.$(\pm X) \pm ( \pm Y)$ . The n+1 bit is the overflow bit used to determine the relative magnitutes of X and Y. It is not used in the computation of Z as the nth bit of all sign magnitude numbers indicate whether the given number is positive or negative number. Hence, the number of bits required to REPRESENT Z is n although one would require n+1 bits for computation of addition or subtraction of X and Y. Correct Ans is A) n bits.
There are 3 other questions with ambiguous answer : Q. 29, 40, 50.