What is a quick moving horned deer like animal native to Africa and Asia?

The animal you're describing is most likely the gazelle.

Here's why:

* Quick moving: Gazelles are known for their incredible speed and agility, able to reach speeds up to 60 mph in short bursts.

* Horned: Both male and female gazelles have horns, though the male's are typically larger and more curved.

* Native to Africa and Asia: There are numerous gazelle species found in various habitats across both continents.

There are many different types of gazelles, each with unique characteristics, but they all share these basic traits.