Answer
If human height were quantized in 1-foot increments, (iii) the child's height would increase in "jumps" of 1 foot at a time as she grows up.
Work Step by Step
The fact human height is quantized in 1-foot increments means that human can only grow by 1 foot at a time. If a child were $x$ (foot) high in day 1, then in day 2, if she grew up, her height would $x+1$ foot, or $x+2$ foot, or etc. In other words, there's no way that her height would be $x+0.1$ foot, or $x+1.5$ foot, etc. in day 2.
Therefore, (iii) is the answer.
This question shows how matter absorbs or emits energy only in quantized quantities.
