Let $p, q, r$ and $s$ be natural numbers such that $p - 2016 = q + 2017 = r - 2018 = s + 2019$ Which one of…
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?
$p$
$q$
$r$
$s$
Solution
Let the common value be $k$. Then $p = k + 2016$, $q = k - 2017$, $r = k + 2018$, $s = k - 2019$. The largest is the one with the largest added constant, which is $r = k + 2018$. Hence $r$ is the largest.