🧮 CSAT — TEXTBOOK DEPTH (Formulas & Techniques, Topic-by-Topic)

The deep-dive companion to the CSAT Maths and CSAT Reasoning notes. CSAT (Paper II) is qualifying at 33%, but failing it ends your attempt — so this is a guaranteed-clear paper if you master a small, closed set of tools. This file gives the formulas and techniques; then drill previous-year papers.

Exam-day order: Comprehension → easy Reasoning → easy Arithmetic (secure 33%) → Data Interpretation → leave long puzzles for last.

PART A — QUANTITATIVE APTITUDE (formulas)

A1. Number system & basics

Divisibility: by 2 (last digit even), 3 (digit sum ÷ 3), 4 (last two digits), 5 (ends 0/5), 6 (2 & 3), 8 (last three digits), 9 (digit sum ÷ 9), 11 (alternating sum).
HCF & LCM: HCF × LCM = product of the two numbers; use HCF for "greatest that divides", LCM for "least common event / when they meet again".
Averages: average = sum ÷ count; average of the first n natural numbers = (n+1)/2. If one value changes, new sum = old sum ± change.

A2. Percentage, profit & loss, interest

Percentage: x% of y = xy/100. % increase/decrease = (change/original) × 100. A change of +a% then −a% gives a net −(a²/100)% (always a loss).
Profit/Loss: Profit% = (Profit/CP) × 100; SP = CP × (100 ± Profit/Loss%)/100. Successive discounts a% then b% → net = a + b − ab/100 (as a discount).
Simple Interest: SI = PRT/100. To double at SI, R×T = 100.
Compound Interest: A = P(1 + R/100)ⁿ; CI = A − P. For 2 years, CI − SI = P(R/100)².

A3. Ratio, proportion, mixtures

Ratio: a:b; if a:b and b:c given, combine to a:b:c. Proportion: a:b = c:d → ad = bc.
Partnership: profit is shared in the ratio of (capital × time).
Alligation (mixtures): (cheaper mean : dearer mean) rule to find the mixing ratio.

A4. Time, speed, distance & work

Speed = distance/time. Unit conversion: 1 km/h = 5/18 m/s.
Relative speed: same direction → subtract; opposite → add. A train crossing a pole covers its own length; crossing a platform covers length + platform.
Boats & streams: downstream = (boat + stream); upstream = (boat − stream).
Time & work: if A does a job in n days, A's one-day work = 1/n. Together (1/a + 1/b). Work ∝ (men × days × hours) — the chain rule: (M₁D₁H₁)/W₁ = (M₂D₂H₂)/W₂.

A5. Mensuration (memorise)

 Rectangle: area = l×b, perimeter = 2(l+b)
 Square: area = a², diagonal = a√2
 Triangle: area = ½ × base × height; equilateral = (√3/4)a²
 Circle: area = πr², circumference = 2πr
 Cuboid: volume = l×b×h, surface = 2(lb+bh+hl)
 Cube: volume = a³, surface = 6a²
 Cylinder: volume = πr²h, curved surface = 2πrh
 Sphere: volume = (4/3)πr³, surface = 4πr²   ;   Cone: volume = (1/3)πr²h

A6. Permutations, combinations & probability

Permutation (order matters): ⁿPᵣ = n!/(n−r)!. Combination (order doesn't): ⁿCᵣ = n!/[r!(n−r)!].
Probability = favourable/total (between 0 and 1). P(A or B) = P(A)+P(B)−P(A and B); for independent events P(A and B) = P(A)×P(B).

A7. Data Interpretation (technique)

Read the units, title and legend first; note whether it's absolute values or percentages. Approximate before calculating; use percentage-change shortcuts; watch for "which is greatest/least" traps. Practise tables, bar/line/pie charts, and caselets.

PART B — LOGICAL REASONING (techniques)

B1. Series & analogies

Number series: check for +, −, ×, ÷, squares/cubes, alternating patterns, and differences of differences.
Letter/analogy: map letters to positions (A=1 … Z=26); look for +n shifts, mirror letters (A↔Z), and relationships (part-whole, cause-effect).

B2. Coding-decoding

Letter shift (e.g., +1: A→B); positional (A=1); substitution (word ↔ code); apply the rule to every letter, including the last (a common trap).

B3. Blood relations & directions

Blood relations: draw a family tree; "only son/daughter of" = the person themselves; use +/− for generations, and symbols for male/female.
Directions: draw a compass; track net displacement; use the Pythagoras theorem for shortest distance; remember left/right turns relative to facing.

B4. Syllogisms

Use Venn diagrams. A conclusion follows only if it is true in every possible diagram. "Some A are B" ⇒ "Some B are A" (valid); "All A are B" does not imply "All B are A". Beware "possibility" conclusions.

B5. Seating arrangement & puzzles

Linear/circular seating: fix the definite clues first, then place relative clues; for a circle, note whether people face the centre (then "right" is clockwise or anticlockwise accordingly). Floor/scheduling puzzles: build a grid; eliminate systematically.

B6. Ordering, ranking & data sufficiency

Ranking: "position from the other end = total − position + 1"; overlaps count a person once.
Data sufficiency: decide whether statement I alone, II alone, both, or neither is sufficient — do not solve fully, just test sufficiency.

PART C — COMPREHENSION & DECISION-MAKING

C1. Reading Comprehension (the highest-accuracy block)

Read actively; mark the thesis (usually first/last sentence of a paragraph); circle contrast markers (but, however, although) — the author's real position follows them; note qualifiers (some, often, may) — correct answers are usually qualified, not absolute.
Answer strictly from the passage, never from outside knowledge. The five traps: extreme options (always/never/only), outside-scope, partially-correct, distortion (qualified → absolute), and reversal.

C2. Decision-making & interpersonal (no negative marking)

These questions carry no negative marking — attempt every one. Choose the option that is ethical, legal, practical, and balanced; avoid extremes (neither harshly rigid nor a total pushover); prefer consultation and following due process.

Preparation plan

 Daily     20 min mental math (tables to 20, squares to 30, %↔fraction)
           + 1 RC passage + 10 reasoning questions
 Weekly    1 full previous-year CSAT paper, timed
 2 months out  solve the last 10 years' CSAT papers under exam conditions
 Target    ~30 confident correct = comfortably above the 66.67/200 cut-off

📚 References & Further Reading

Standard practice: RS Aggarwal (Quantitative Aptitude; Verbal & Non-Verbal Reasoning), Arihant/Disha CSAT, TMH GS Paper II
The single best resource: previous years' CSAT papers (last 10–12) — upsc.gov.in
Base concepts: NCERT Maths VI–X (free PDF)