TMUA 2022 · Paper 1 · Question 16

In this question, $a_{1}, \dots, a_{100}$ and $b_{1}, \dots, b_{100}$ and $c_{1}, \dots, c_{100}$ are three sequences of integers such that

a_{n} \leq b_{n} + c_{n}

for each $n$ . Which of the following statements must be true?

I $(minimum of a_{1}, \dots, a_{100}) \leq (minimum of b_{1}, \dots, b_{100}) + (minimum of c_{1}, \dots, c_{100})$

II $(minimum of a_{1}, \dots, a_{100}) \geq (minimum of b_{1}, \dots, b_{100}) + (minimum of c_{1}, \dots, c_{100})$

III $(maximum of a_{1}, \dots, a_{100}) \leq (maximum of b_{1}, \dots, b_{100}) + (maximum of c_{1}, \dots, c_{100})$

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