Maximise or minimise one value given an average and distinct/bounded others

CAT has tested this idea 8 times across 8 papers, from 2018 to 2022. Solve one, and the others are the same method with different numbers or wording, which is why repeated concepts are the most efficient thing to practise.

Question	What it asks	Answer
CAT 2021 Slot 3 · QA Q7	five equal toppers, others distinct, lowest 30	92
CAT 2022 Slot 2 · QA Q16	five distinct marks, three above 32; Amit lowest	C
CAT 2020 Slot 3 · QA Q17	batsman's innings below 38; smallest lowest score	C
CAT 2022 Slot 3 · QA Q13	six distinct naturals; averages of two smallest and largest	A
CAT 2018 Slot 2 · QA Q2	52 increasing integers; largest possible first term	D
CAT 2019 Slot 2 · QA Q2	20 of 30 integers at most 5; max of their average	C
CAT 2018 Slot 1 · QA Q34	people above and below 51; largest average of younger	D
CAT 2020 Slot 2 · QA Q3	means of lowest 9 and highest 9; range of overall mean	C

Part of Ratio, Mixtures & Averages (84 questions since 2017).