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Question 10 : 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 possibly evaluate to?

- 0
- 9
- 6
- 4
- 1

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W^{4 }+ X^{3 }+ Y^{2 }+ Z ≤ 4

We can isolate the terms as W^{4 }+ Y^{2}+ X^{3} + Z ≤ 4

From here we can see that the equalities [2] and [3] together make up [1]

From inequation [2],

Z can be 1 or 2 and X can be 0 or 1

W | X | Y | Z |

- | 1 | - | 1 |

- | 0 | - | 2 |

From inequation [3],

Y can only be -1 as Y is negative and thus cannot be 0 or lesser than -1 or the inequality wouldn't be satisfied. W can be -1 or 1 and

W | X | Y | Z |

-1 | 1 | -1 | 1 |

-1 | 0 | -1 | 2 |

1 | 1 | -1 | 1 |

1 | 0 | -1 | 2 |

So we are left with,

W | X | Y | Z |

±1 | 0 | -1 | 2 |

From here we can calculate the value of W

Choice C is the correct answer.

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