**Core Concept**
Viruses are acellular particles that can cause infections in humans. They have genetic material either in the form of DNA or RNA, which is responsible for their replication and transcription.

**Why the Correct Answer is Right**
The question asks for an organism that does not possess both DNA and RNA. The correct answer to this question can be found by considering the types of genetic material present in different viruses. Most viruses have either DNA or RNA as their genetic material, but not both. For example, Herpesviruses have DNA, while Influenza viruses have RNA.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because some viruses, like Adenoviruses, possess both DNA and RNA.
**Option B:** This option is incorrect because some viruses, like Retroviruses, possess both DNA and RNA, but in a unique way - their genetic material is initially RNA, which is then reverse-transcribed into DNA.
**Option C:** This option is incorrect because some viruses, like Poxviruses, possess both DNA and RNA.

**Clinical Pearl / High-Yield Fact**
Remember that viruses have diverse genetic materials, and it's essential to know the specific characteristics of each virus to understand their replication and transmission.

**Correct Answer: D. None of the above options**