If 2^20 = 2^15 x+y, where x and y are non-negative integers,

|x−y| represents the distance between points x and y on a number line.

Before we move onto the problem, lets take an example.

Let the distance between two points on a number line be 5.

Assume that one of the point is x and the other is y (also x > y). We know that the distance between these two points is 5. This statement can be represented mathematically as -

x - y = 5

Now if x is twice as far from y, we can denote the distance between them as 2x - y. And logically we know that the distance between them will now be 10.

In the form of an equation, this relationship is written as -

2x - y = 10

The distance between x and y is thus \(\frac{1}{2}\) * 10

Similarly if x is thrice as far from y, the distance is denoted by 3x - y

3x - y = 15

However as we have seen in the previous example, the distance between x and y can be denoted as \(\frac{1}{3}\) * 15

If we apply the same concept to the above problem we can now read the problem as

"The distance between \(2^{15}\) times x and y is \(2^{20}\)"

\(2^{20}\) = \(2^{15}\)x + y

Therefore the distance between x and y can denoted as -

|x - y| = \(\frac{1 }{ 2^{15} }* 2^{20}\)

|x - y| = \(2^5\)

IMO - C