XAT 2022 Number System — Previous Year Question

Wilma, Xavier, Yaska and Zakir are four young friends, who have a passion for integers. One day, each of them selects one integer and writes it on a wall. The writing on the wall shows that Xavier and Zakir picked positive integers, Yaska picked a negative one, while Wilma’s integer is either negative, zero or positive. If their integers are denoted by the first letters of their respective names, the following is true: $W^4 + X^3 + Y^2 + Z \le 4$ $X^3 + Z \ge 2$ $W^4 + Y^2 \le 2$ $Y^2 + Z \ge 3$ Given the above, which of these can $W^2 + X^2 + Y^2 + Z^2$ possibly evaluate to?