How should I approach this question ?

Hi Ryan,

Here is no specific approach, you need to know the basics of Modulus and inequalities. We can do plug in, but still we need to know the basics.

Below is my explanation.

Statement I is insufficient:

|x−3|≥y.

As given that y is non negative value then |x−3| is more than (or equal to) some non negative value. So we cannot determine single numerical value of x.

So,Not sufficient.

Or else you can open the modulus and  check |x−3 |≥ y ≥ 0 whether it is sufficient

x−3 ≥ y ≥ 0

when x−3>0

then  x>3

OR

−x+3 ≥ y ≥ 0

when x−3<0

i.e.,  x<3

So, Insufficient.

Statement II is sufficient:

|x−3| ≤ −y.

Now, as |x−3| is never negative (0 ≤ |x−3|)

then 0 ≤ −y this becomes y ≤ 0, but in question its given that y ≥ 0 , so then only option is y has to be zero.

|x−3| ≤ 0

|x−3|=0=y

x−3=0

x=3.

So the Answer is B.

Hope this helps.