# XAT 2022 Question Paper | Quantitative Aptitude and Data Interpretation

###### XAT Previous Year Paper | XAT QADI Questions | Question 10

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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?

1. 0
2. 9
3. 6
4. 4
5. 1

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W4 + X3 + Y2 + Z ≤ 4
We can isolate the terms as W4 + Y2+ X3 + 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
From inequality [4] we can rule out the possibilities 1 and 3 as Y3 + Z is not greater than 3 in these possibilities.
So we are left with,

 W X Y Z ±1 0 -1 2

From here we can calculate the value of W2 + X2 + Y2 + Z2
= 6

Choice C is the correct answer.

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