Final answer:
David's sex chromosomes are XY, and Katie's sex chromosomes are XX, in alignment with typical sex chromosome arrangement in males and females, resulting in their respective male and female biological development.
Step-by-step explanation:
If David and Katie are fraternal twins with normal biological development before birth, then David's sex chromosomes are XY, and Katie's sex chromosomes are XX.
In the embryonic development stage, sex is determined by the pairing of sex chromosomes; males carry XY chromosomes, while females carry XX chromosomes. The Y chromosome triggers the development of male characteristics, whereas its absence (two X chromosomes) results in the development of female characteristics. This chromosome pairing is visible in karyotypes and is pivotal for sexual differentiation. Moreover, rare chromosomal disorders can arise from nondisjunction, where individuals may have extra sex chromosomes, like XXY in Klinefelter syndrome or just a single X chromosome as in Turner syndrome, affecting physical and reproductive development.