Wilma, Xavier, Yaska and Zakir are four young friends, who have a passion for integers. One day, each of them

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:

$W^{4}+X^{3}+Y^{2}+Z\leq4$
$X^{3}+Z\geq2$
$W^{4}+Y^{2}\leq2$
$Y^{2}+Z\geq3$
Given the above, which of these can $W^{2}+X^{2}+Y^{2}+Z^{2}$ possibly evaluate to?

Accepted Answer

6. Given that X, Z are positive Y is negative and W can be either positive or zero or negative. The given conditions are : W 4 + X 3 + Y 2 + Z ≤ 4 W^{4}+X^{3}+Y^{2}+Z\leq4 W 4 + X 3 + Y 2 + Z ≤ 4 X 3 + Z ≥ 2 X^{3}+Z\geq2 X 3 + Z ≥ 2 W 4 + Y 2 ≤ 2 W^{4}+Y^{2}\leq2 W 4 + Y 2 ≤ 2 Y 2 + Z ≥ 3 Y^{2}+Z\geq3