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?
- (a) p
- (b) q
- (c) r ✓ UPSC's answer
- (d) s
Why the answer is (c)
• Let the common value of the expressions be $k$.
• From $p - 2016 = k$, we get $p = k + 2016$.
• From $q + 2017 = k$, we get $q = k - 2017$.
• From $r - 2018 = k$, we get $r = k + 2018$.
• From $s + 2019 = k$, we get $s = k - 2019$.
• Comparing the coefficients added to $k$, $2018$ is the largest positive constant, making $r$ the largest number.
• Therefore, $r$ is the largest natural number among the four.
Why the other options are wrong
- (a) p
- p is equal to k + 2016, which is less than r (k + 2018).
- (b) q
- q is equal to k - 2017, which is significantly smaller than r.
- (d) s
- s is equal to k - 2019, which is the smallest of the four numbers.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.