TMUA 2017 · Paper 2 · Question 13

The positive real numbers $a \times 1 0^{- 3}$ , $b \times 1 0^{- 2}$ and $c \times 1 0^{- 1}$ are each in standard form, and

(a \times 1 0^{- 3}) + (b \times 1 0^{- 2}) = (c \times 1 0^{- 1}) .

Which of the following statements (I, II, III, IV) must be true?

I $a > 9$

II $b > 9$

III $a < c$

IV $b < c$