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:

Given the above, which of these can W^{2} + X^{2} + Y^{2} + Z^{2} possibly evaluate to?

A 9

B 0

C 4

D 6

E 1

## EXPLANATION

D

Given that X, Z are positive Y is negative and W can be either positive or zero or negative.

The given conditions are :

For W^{4}+Y^{4} ≤ 2 Since Y is negative but Y^{2} is always positive and must be less than 2 because W^{4} is a non negative value. Hence Y = -1 is the only possibility. For W this can take any value among -1, 0, 1.

Y^{2} + Z^{2 }≥ 3 Since Y = -1, Z must be at least equal to 2 so the value of Y ^{2}+ Z ≥ 3 is greater than 2. X is a positive value and must at least be equal to 1.

The condition: W^{2} + X^{2} + Y^{2} + Z^{2} here has all the independent values nonnegative.

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