**Core Concept**
A balanced translocation between chromosomes 15 and 21 in one of the parents increases the risk of producing gametes with an unbalanced translocation, which can lead to Down syndrome in offspring. This is due to the increased likelihood of meiotic errors during gametogenesis.

**Why the Correct Answer is Right**
In individuals with a balanced translocation, the chromosomes do not have a complete set of genes, which can lead to the formation of abnormal gametes with an unbalanced translocation. If these gametes are fertilized, the resulting offspring may have Down syndrome. Couples with a history of balanced translocations should undergo genetic counseling and consider prenatal testing to assess the risk of Down syndrome in their children.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because it does not address the underlying genetic issue of balanced translocations. While avoiding advanced maternal age may reduce the risk of Down syndrome, it does not eliminate the risk in couples with a family history of balanced translocations.
* **Option B:** This option is incorrect because it does not provide any specific advice or guidance for the couple. Simply stating that they should "avoid pregnancy" is not a helpful or informed response.
* **Option C:** This option is incorrect because it does not take into account the genetic predisposition of the couple. While prenatal testing may be recommended, it is not the only advice that should be provided to the couple.

**Clinical Pearl / High-Yield Fact**
Couples with a history of balanced translocations should undergo genetic counseling and consider prenatal testing to assess the risk of Down syndrome in their children. This can include chromosomal analysis, ultrasound, and maternal serum screening.

**Correct Answer: C. Prenatal testing and genetic counseling.**