Final answer:
The egg cell is responsible for passing on mutations to offspring, as it is a germ cell that merges with a sperm cell during fertilization, potentially carrying hereditary information.
Step-by-step explanation:
The type of cell that can pass on mutations to offspring is the egg cell. Red blood cells, skin cells, and nerve cells are all examples of somatic cells, which when mutated only affect the individual and the descendants of those mutated cells, without affecting offspring. In contrast, germ cells like egg cells and sperm can pass germline mutations to future generations, with the potential to manifest in every cell of the offspring's body. This can lead to hereditary diseases or contribute to the genetic variation within a population.