Let p, q, r and s be natural numbers such that
p – 2016 = q + 2017 = r – 2018 = s + 2019
Which one of the following is the largest natural number?

The correct option is r.

To find which of the natural numbers $p$, $q$, $r$, and $s$ is the largest, let us set the given equal expressions equal to a single constant, say $k$.

We are given the relation:
$p-2016=q+2017=r-2018=s+2019=k$
where $k$ is a constant value.

Now, express each variable in terms of $k$:

1. From $p-2016=k$:
$p=k+2016$

2. From $q+2017=k$:
$q=k-2017$

3. From $r-2018=k$:
$r=k+2018$

4. From $s+2019=k$:
$s=k-2019$

Now, let us compare the values of $p$, $q$, $r$, and $s$:

• $r=k+2018$
• $p=k+2016$
• $q=k-2017$
• $s=k-2019$

Since $2018>2016>-2017>-2019$, adding $2018$ to $k$ yields the largest result among all expressions.

Therefore, $r$ is the largest natural number.