Just like it is important to flesh out your prompt, it is equally important to flesh out (I) and (II) in the context of the question. Let’s look at another example:

x=y+1 what is the value of xy?

(I) x^{2 }= y + 1

(II) x = √ (y+1)

The prompt is pretty straightforward. We are looking for the value of xy and we know that x=y+1, so we can also say we are looking for y(y+1), or that if we know the value of one of the numbers, we can figure out the value for the other and thus the product.

We’ll start by going over (I), we can actually set x and x^{2} equal to each other, because they both are equal to y+1. x= x^{2 }yields two solutions for x, 1 and 0. This might lead you to think that we cannot determine what xy is. However, if we put this in context of the question we will discover that this is not the case.

If x=0, then y=-1, therefore the value of xy=0

If x=1, then y=0 and the value of xy is also 0

So, even though we don’t know the value of x, we still know the value of xy, so (I) is actually sufficient.

For continuity’s sake, lets also look at (II), which tells us that x = √ (y+1). This means that

y+1 = √ (y+1) Therefore y+1= 1 or 0 and y=0 or -1

We also know that if y=0 then x=1 and xy=0

And if y=-1 then x=0 and xy is still 0

Thus each of the options is sufficient on their own. Had we not taken the time to multiply them, out we would have gotten this question wrong.