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?

Correct Option (3)

Let the common value of the given expression be $k$.
$$p-2016=q+2017=r-2018=s+2019=k$$
From this, each variable can be expressed in terms of $k$:

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

To identify the largest natural number, we compare the constant terms associated with $k$. The constants are $+2016$, $-2017$, $+2018$, and $-2019$. The largest among these constants is $+2018$. Consequently, $r=k+2018$ represents the largest natural number.

Incorrect Options:

Based on the expressions derived:

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

Comparing these with $r=k+2018$:

• Since , $p$ is less than $r$.
• Since , $q$ is less than $r$.
• Since , $s$ is less than $r$.

The complete order from smallest to largest is . Therefore, $p,q,$ and $s$ are not the largest natural numbers.