MPT — Analytical / Reasoning | CSS MPT Notes

What this covers

Two related but distinct categories from your book: Logical Problem Solving (structure/strategy-based) and Analytical Problem Solving (relationship-based). Both test reasoning speed, not memorized facts.

Quick Outline

Logical Problem Solving

Structure

Logical problems usually give you a set of statements/rules, then ask you to determine what must be true, could be true, or cannot be true.

Strategies

Draw it out — tables, diagrams, or number lines beat mental tracking every time
Eliminate, don't guess — cross off options that violate any given rule
Test the extremes first — try the most restrictive condition, it narrows options fastest
Watch for "must be true" vs "could be true" — these require different logic (must = true in ALL valid arrangements; could = true in AT LEAST ONE)

Suggested Approach (step-by-step)

Read all conditions before touching any question
List out fixed/certain facts first
Build a skeleton (grid/diagram) from the fixed facts
Apply conditional statements one at a time
Only then attempt the questions

Series & Patterns — Series & Patterns

Number series: find the rule (add/subtract/multiply constant, or a changing difference)
- Example: 2, 5, 10, 17, 26... (differences: 3,5,7,9 — add consecutive odd numbers) → next = 26+11 = 37
Letter series: track position shifts (A=1, B=2...Z=26)
- Example: B, D, F, H... (skip 1 letter) → next = J
Mixed series: alternating pattern between two interleaved series
- Example: A, 1, C, 3, E, 5... → next = G

Coding–Decoding — Coding–Decoding

Letter shift coding: each letter shifted by a fixed number
- Example: if CAT = DBU (each letter +1), decode FOG using same rule → GPH
Number coding: letters assigned position values, then combined/manipulated
Word/symbol substitution: given a full substitution key, decode a new word

Direction & Distance — Direction & Distance

Standard compass: N, S, E, W (and NE, NW, SE, SW between them)
Track turns carefully: Right turn from North → East; Left turn from North → West
Use Pythagoras for shortest/final distance (not total path walked)
- Example: Walk 3 km North, then 4 km East → shortest distance back

\sqrt{3^2+4^2}=5 \text{ km}

Blood Relations — Blood Relations

Draw a family tree as you read — never solve mentally
Key terms: "mother's brother" = maternal uncle; "father's sister's son" = cousin
Example: "A is B's father. B is C's sister. How is A related to C?" → A is C's father

Syllogism (basic) — Syllogism

Two statements (premises) + a conclusion to evaluate
Common forms: "All A are B" / "Some A are B" / "No A are B"
Rule: "All A are B" does NOT mean "All B are A" (one-directional)
Example: "All cats are animals. All animals need food. Therefore, all cats need food." → Valid (chain logic)
Example trap: "Some students are athletes. Some athletes are tall. Therefore, some students are tall." → Invalid (the "some" groups may not overlap)

Statement–Conclusion — Statement–Conclusion

Only use information given in the statement — don't bring outside knowledge/assumptions
"Follows" = must be logically true from the statement alone
Common trap: a conclusion that sounds true in real life but isn't actually stated

Analytical Problem Solving

General Types of Questions

Grouping/classification — sort items into categories based on given rules. Grouping & Classification
Sequencing/ordering — arrange people/items in order (rank, queue, schedule) based on clues. Sequencing & Ordering
Comparison — "who is taller/older/richer than whom" chains. Comparison
Matching — match items across two or more categories (e.g., person → city → profession). Matching

Most Frequent Relationships Tested

Greater than / less than chains (age, height, rank)
Before/after sequencing (time, order of events)
Same group / different group (categorization)
Direct vs indirect relationships (e.g., "twice as many as", "three more than")

Strategies

Convert words to symbols immediately — "A is older than B" → A > B
Chain the relationships — combine all clues into a single ordered list before answering
Use a grid for matching problems — rows = one category, columns = another, mark ✓/✗ as you eliminate
Don't assume order from how clues are listed — the clues are rarely given in solved order

Worked Example (Ordering)

A is taller than B. C is shorter than B. D is taller than A. Who is the shortest?

D > A > B > C → C is the shortest

Worked Example (Matching)

Ali, Bilal, and Sara each like a different fruit: mango, apple, banana.

Ali does not like mango.

Sara likes apple.

Bilal does not like banana.

Sara = apple (given)
Ali ≠ mango, so Ali = banana (since apple is taken)
Bilal = mango (last remaining, consistent with "not banana")

Drill Set

Series: 3, 6, 12, 24, ? — 48 (×2 pattern)
Series: Z, X, V, T, ? — R (skip 1 letter backward)
Coding: If DOG = EPH (+1 each letter), code CAT — DBU
Direction: Walk 6 km South, then 8 km West. Shortest distance to start?

\sqrt{6^2+8^2}=10 \text{ km}

Blood relation: "A is B's son. C is A's sister. How is C related to B?" — Daughter
Syllogism: "All doctors are educated. Some educated people are rich. Therefore some doctors are rich." — Invalid (no direct link established)
Ordering: X is older than Y. Y is older than Z. Who is youngest? — Z
Ordering: If P > Q, Q > R, and R > S, who is the smallest? — S