Set Theory Two Item Preferences

Total $U = 200$, $P = 105$, $B = 134$. Let $x$ be number of students who like both. Only Burger = $134 - x$. Only Pizza = $105 - x$. Neither = $200 - (105 + 134 - x) = x - 39$. For non-negative regions: $x \ge 39$ $105 - x \ge 0 \Rightarrow x \le 105$. So $39 \le x \le 105$. Only Burger = $134 - x$. Since $39 \le x \le 105$, subtract from 134: $134 - 105 \le 134 - x \le 134 - 39 \Rightarrow 29 \le \text{Only Burger} \le 95$. Looking at options, 93 lies in $[29, 95]$.