Integers Actual Question in XAT 2022
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 W2 + X2 + Y2 + Z2 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 W4+Y4 ≤ 2 Since Y is negative but Y2 is always positive and must be less than 2 because W4 is a non negative value. Hence Y = -1 is the only possibility. For W this can take any value among -1, 0, 1.
Y2 + Z2 ≥ 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: W2 + X2 + Y2 + Z2 here has all the independent values nonnegative.
