**Core Concept**
The hardness of a material is a measure of its resistance to plastic deformation, and various tests are used to assess this property. Brittle materials are those that exhibit little to no plastic deformation before fracturing, and as such, a hardness test that is suitable for ductile materials may not be applicable.

**Why the Correct Answer is Right**
The Vickers hardness test (Option B) and the Rockwell hardness test (Option C) are commonly used for testing the hardness of both ductile and brittle materials. However, the Shore hardness test (Option D) is primarily used for testing the hardness of rubber and other elastomers, which are ductile materials. The Brinell hardness test (Option A) is also used for testing ductile materials and is not suitable for brittle materials.

**Why Each Wrong Option is Incorrect**
**Option A:** The Brinell hardness test is used for testing the hardness of ductile materials by measuring the diameter of the indentation created by a steel ball.
**Option B:** The Vickers hardness test is used for testing the hardness of both ductile and brittle materials by measuring the area of the indentation created by a diamond pyramid.
**Option C:** The Rockwell hardness test is used for testing the hardness of both ductile and brittle materials by measuring the depth of penetration of an indenter under a known load.
**Option D:** The Shore hardness test is not primarily used for testing the hardness of brittle materials, which do not exhibit plastic deformation before fracturing.

**Clinical Pearl / High-Yield Fact**
When working with brittle materials, it's essential to use a hardness test that is specifically designed for such materials, as using a test intended for ductile materials can lead to inaccurate results.

**Correct Answer:** A. Brinell hardness test.