XAT 2022 Question Paper | Quantitative Aptitude and Data Interpretation

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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?

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Video Explanation

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Explanatory Answer

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

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The answer is '6'

Choice C is the correct answer.