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?

Answer: C

Method I:

In questions like this, keep in mind that you are just supposed to compare the numbers, so avoid wasting time in finding their real values.

p - 2016 = q + 2017

or p = q + 2017 + 2016 (it means p > q)

q + 2017 = r - 2018

or r = q + 2017 + 2018 (it means r > q)

r - 2018 = s + 2019

or r = s + 2019 + 2018 (it means r > s)

p - 2016 = r - 2018

or r = p - 2016 + 2018 = p + 2 (it means r > p)

We already know that r > q, s

Hence, r is the largest number.

Method II:

Let s = 0.

So, we get:

p - 2016 = q + 2017 = r - 2018 = 2019

So, p - 2016 = 2019

or p = 2019 + 2016 = 4035

and q + 2017 = 2019

or q = 2019 - 2017 = 2

and r - 2018 = 2019

or r = 2019 + 2018 = 4037

Hence, r is the largest number.