How is my father's brother's only sibling's mother related to my sister's only brother?

Introduction / Context:
This blood relation question looks complicated because of the long chain of possessives such as my father's brother's only sibling's mother. However, each step simply moves one generation up or sideways. The key skill tested is your ability to expand the chain slowly, replace each phrase with a simpler relation and keep track of who is who relative to the reference person, which here is the speaker (me).

Given Data / Assumptions:
- Reference person: me. - Phrase 1: my father's brother. - Phrase 2: that brother's only sibling. - Phrase 3: the mother of that only sibling. - Comparison person: my sister's only brother. - We assume a simple family where words like father, brother, sister are used in their usual sense.

Concept / Approach:
We must identify two people: the person described by my father's brother's only sibling's mother and the person described by my sister's only brother, and then determine how the first is related to the second. The simplest method is to decode both parts separately. Often, my sister's only brother ends up being the speaker himself, and the long chain on the other side collapses to a close ancestor such as grandmother.

Step-by-Step Solution:
Step 1: My sister's only brother: if I (the speaker) am male, then my sister has exactly one brother, namely me. So my sister's only brother = me. Step 2: My father's brother is my paternal uncle. Step 3: My father's brother's only sibling: the only sibling of my paternal uncle must be my father (since he is that uncle's brother). Step 4: The mother of that only sibling is the mother of my father, that is, my paternal grandmother. Step 5: From Step 1, we know the comparison person is me, so we now ask: how is my father's brother's only sibling's mother related to me? She is my grandmother.

Verification / Alternative check:
You can draw a small family tree: put yourself in the middle, your father above you, your father's brother next to him, and your grandmother above them. The chain father's brother's only sibling's mother clearly goes up to your grandmother. On the other side, my sister's only brother is obviously you, assuming a typical exam setting where the speaker is male. This visual check confirms that the relation is grandmother.

Why Other Options Are Wrong:
- Neice: A niece is a female child of a sibling. That does not fit an elderly ancestor like the mother of your father. - Aunt: An aunt would be your father's sister or your uncle's wife, not the mother of your father. - Mother: Your father's mother is one generation above your mother and father, not your own mother. - Sister: A sister would be on the same generation as you, again not matching an ancestor.

Common Pitfalls:
Typical errors include confusing my father's brother with my brother, or forgetting that the only sibling of my father's brother is my father himself. Students may also misinterpret my sister's only brother as some other person instead of the speaker. Working systematically, replacing each phrase with a family label and, if needed, sketching a tiny tree will prevent these mistakes.

Final Answer:
The lady described is the grandmother of my sister's only brother (that is, my grandmother).