Family Tree Problems: Mental Ability Test (MAT) Notes for NTSE

Family Tree Problems

NTSE – Mental Ability Test (MAT)

A systematic guide to solving family‑tree questions in the NTSE exam.

1. Simple Explanation

A family tree is a diagram that shows the relationships between people across generations.
In an NTSE question you are usually given a small tree (or a description of one) and asked to:

Identify the relationship between two persons (e.g., great‑grand‑uncle, first cousin once‑removed).
Count how many people belong to a certain generation or a specific branch.
Determine the position of a person in the tree (depth, height, sibling index, etc.).

The key is to remember that a family tree is a rooted tree in graph theory, where:

Symbol	Meaning
Root	The earliest ancestor (usually the oldest person).
Parent	The immediate ancestor of a person.
Child	The immediate descendant.
Sibling	Two people who share the same parent.
Ancestor	Any parent, grand‑parent, great‑grand‑parent, …
Descendant	Any child, grand‑child, great‑grand‑child, …
Generation	All people at the same distance from the root.

2. Key Points to Remember

#	Concept	Quick Hint
1	Generation Index	Root = 0, children = 1, grandchildren = 2, etc.
2	Ancestor/Descendant Count	In a binary tree the number of ancestors of a node at depth d is d; the number of descendants is (2^{(h-d)}-1) where h is tree height.
3	Sibling Count	Two people with the same parent are siblings.
4	Cousin Level	The k‑th cousin is defined by the number of generations back to the common ancestor.
5	Removal	“Once‑removed”, “twice‑removed” refers to a difference of one or two generations between two cousins.
6	Great‑ Prefixes	Each “great‑” adds one generation between the two relatives.
7	Counting with Powers of 2	In a full binary tree: number of people in generation i = (2^i).
8	Tree Traversal	Use depth‑first (DFS) or breadth‑first (BFS) to locate nodes quickly.
9	Common Ancestor	The lowest common ancestor (LCA) of two nodes determines their relationship.
10	Shortcut Rules	- Parent → “Mother / Father” - Sibling → “Brother / Sister” - Child → “Son / Daughter” - Grand‑ → “Grand‑mother / Grand‑father” - Great‑Grand‑ → “Great‑grand‑mother / Great‑grand‑father”

3. Worked Example

Question

In a family tree, A is the mother of B and C.
B is married to D and they have two children: E and F.
C is married to G and they have one child: H.

(i) How many people are in the second generation from A?
(ii) What is the relationship between E and H?

Diagram (simplified)

          A
         / \
        B   C
       / \   \
      E   F   H
     (B+D)  (C+G)

(i) Second Generation from A

Generation 0: A
Generation 1: B, C → 2 people
Generation 2: E, F, H → 3 people

Answer: 3 people.

(If you count all descendants up to generation 2, you get 5 people: B, C, E, F, H. But the question asks only for generation 2.)

(ii) Relationship Between E and H

Find Lowest Common Ancestor (LCA).
A is the only common ancestor of both E and H.
Determine Generations from LCA:
E is 2 generations down from A (A → B → E).
H is 2 generations down from A (A → C → H).
Apply Cousin Rules:
- Same number of generations → First cousins.
- No “removed” because the generation difference is zero.

Answer: E and H are first cousins.

4. Quick Revision Summary

Topic	What to Check
Generation Counting	Use powers of 2 for full binary trees; add 1 for each “great‑”.
Ancestor vs. Descendant	Count nodes on the path to the root vs. below the node.
Sibling Identification	Same parent → sibling.
Cousin Level	(k)-th cousins share a common ancestor (k+1) generations back.
Removal	Difference in generations between the two cousins.
Great‑Prefix	One “great‑” = one additional generation.
Traversal Methods	DFS for depth, BFS for level.
Common Tests	“How many people in nth generation?”, “Relationship between X and Y?”.
Tips	Always sketch the tree; label generations; use the LCA concept.

Practice Question

In a family tree, P has