Complete formula collection for quant aptitude and logical reasoning — used in TCS, Infosys, Wipro, CAT, Banking, SSC placement exams.
Get all 250+ formulas in a printable one-page PDF — perfect for last-minute revision before your placement test!
📊 Advanced Quantitative
Number System, Algebra, Geometry & Mensuration
🧠 Logical Patterns
Complex Puzzles, Seating & Advanced Series
🎯 Practice Sets
Sample problems with detailed solutions
👇 Click on any section below to expand and explore!
Heavily tested in TCS NQT, Infosys, Wipro — master all 6 pattern types
Forward: A=1 → Z=26
A B C D E F G H I J K L M
1 2 3 4 5 6 7 8 9 10 11 12 13
N O P Q R S T U V W X Y Z
14 15 16 17 18 19 20 21 22 23 24 25 26
Reverse: A=26 → Z=1
Formula: Reverse value = 27 − Forward value
A=26, B=25, C=24 … Z=1
💡 Example:
If CAT → 3,1,20 then code = 3120 or C=3, A=1, T=20
A↔Z, B↔Y, C↔X … (sum = 27)
💡 Quick Check:
Position of letter + Position of its opposite = 27
D(4) + W(23) = 27 ✓
+1 Shift (each letter → next):
CAT → DBU (C+1=D, A+1=B, T+1=U)
+2 Shift:
CAT → ECW (C+2=E, A+2=C, T+2=V... wait: T=20, +2=22=V)
Alternating shift (+1, −1, +1...):
CAT → DBT (C+1=D, A+1=B, T−1=S... varies by pattern)
⚡ Wrap-around rule:
Z+1 = A, A−1 = Z (alphabet is circular)
Pattern: Word → Sum of positions
CAT = 3+1+20 = 24
DOG = 4+15+7 = 26
Pattern: Position × 2 or Position²
A=2, B=4, C=6 (×2 pattern)
A=1, B=4, C=9 (square pattern)
Reversal coding:
CAT → TAC (word reversed)
CAT → ZZG (opposite letters)
Step 1: Find the common word in two statements
If "ra sa ta" = "cat sat mat" and "ra pa qa" = "cat dog hat" → ra = cat
Step 2: Eliminate to find remaining
Once one word found, cross-reference to decode others by elimination
⚡ Speed tip:
Always start by finding the word that appears in the MOST statements — it's easiest to decode first
How to solve:
💡 Key insight:
In matrix coding, every row and column digit (0-4) appears exactly once for each letter in the grid
30–40% of TCS NQT is DI — learn to read charts in under 20 seconds
Read axis labels first
What does X-axis represent? What unit is Y-axis? (thousands, lakhs, %)
Note the scale
Each grid line = how much? Misreading scale causes 90% of DI errors
Scan for highest & lowest bar
Usually 1–2 questions ask max/min directly — answer in 5 seconds
Calculate only what's asked
Don't calculate everything upfront. Read the question first, then extract only that data
Central angle of a sector:
= (Value / Total) × 360°
If sales = 240 out of 1200 → angle = (240/1200)×360 = 72°
% represented by sector:
= (Central angle / 360) × 100
72° → (72/360)×100 = 20%
Value from % and total:
= (% / 100) × Total
⚡ Approximation trick:
In DI, round numbers to nearest 5 or 10 for faster mental math. Final answer options are usually far enough apart that approximation is safe.
% change between years:
= [(New − Old) / Old] × 100
Quick: if increase ≈ 1/5 of old → ~20% growth
Ratio comparison (without division):
Cross-multiply: a/b vs c/d → compare a×d vs b×c
240/480 vs 180/400 → 240×400=96000, 480×180=86400 → first ratio is bigger
Average of a column:
Pick a central value, add/subtract deviations, divide by count
Values 48,52,47,53,50 → base=50, deviations: −2,+2,−3,+3,0 → sum=0 → avg=50
Steepest rise / fall:
Visually identify — don't calculate all years. The steepest slope = highest % change.
Intersection point questions:
Two lines cross → both variables equal at that point. Just read the year from X-axis.
CAGR (Compound Annual Growth Rate):
CAGR = [(Final/Initial)^(1/n) − 1] × 100
For MCQs: verify which option gives closest result, don't calculate exact root
🏆 DI Golden Rule:
Spend max 8 minutes per DI set (5 questions). That's 96 seconds/question. If a question needs complex calculation, skip and attempt the visual/easy ones first.
Identify the pattern in under 10 seconds — here's how
Rule: Constant difference between consecutive terms
3, 7, 11, 15, 19 → diff = +4
How to identify: Subtract consecutive terms — all equal
nth term = a + (n−1)d
Rule: Constant ratio between consecutive terms
2, 6, 18, 54 → ratio = ×3
How to identify: Divide consecutive terms — all equal
nth term = a × r^(n−1)
Rule: Terms are squares of consecutive numbers
1, 4, 9, 16, 25, 36, 49, 64, 81, 100
How to identify: √ each term — should be 1,2,3,4...
nth term = n²
Rule: Terms are cubes of consecutive numbers
1, 8, 27, 64, 125, 216, 343
How to identify: ∛ each term — should be 1,2,3,4...
nth term = n³
Rule: Each term = sum of previous two terms
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89
How to identify: term(n) = term(n−1) + term(n−2)
No closed form — memorise first 12 terms
Rule: Differences between terms follow a pattern
2, 5, 10, 17, 26 → diffs: 3,5,7,9 (AP!)
How to identify: Find 1st diff → if AP: series of n²+1
Check if 2nd differences are constant
Rule: Two interleaved series (odd & even positions)
2, 9, 4, 16, 8, 25 → 2,4,8 (×2) & 9,16,25 (n²)
How to identify: Separate odd-position & even-position terms
Solve each sub-series independently
Rule: Terms are consecutive prime numbers
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
How to identify: Check each term for primality
Memorise primes up to 100
Rule: +n, ×n or alternating add/multiply pattern
1, 2, 6, 24, 120 → ×2, ×3, ×4, ×5 (factorials!)
How to identify: Try ratio → if not constant, try ratio+constant
n! = 1, 2, 6, 24, 120, 720, 5040...
Step 1: Find differences (a₂−a₁, a₃−a₂...)
Step 2: Find ratios (a₂/a₁, a₃/a₂...)
Step 3: Find differences of differences
Step 4: Separate odd & even position terms
Follow these frameworks — solve any puzzle in 2–4 minutes
Template:
_ _ _ _ _ _ _
1 2 3 4 5 6 7
Draw blank boxes, number them left to right
Solving order:
1️⃣ Place fixed positions first (A is at position 3)
2️⃣ Place relative positions (B is immediately right of A)
3️⃣ Place negative constraints last (C is NOT next to D)
4️⃣ Use remaining clues to fill gaps by elimination
⚡ Key terms:
"Immediate left/right" = adjacent | "2nd to the left" = gap of 1 between
Facing inward (default):
Right of A = clockwise from A
Left of A = anticlockwise from A
Facing outward:
Right of A = anticlockwise from A (OPPOSITE!)
Left of A = clockwise from A
Template approach:
1️⃣ Fix one person at any position (reference point)
2️⃣ Place directly stated neighbors next
3️⃣ "Opposite in a circle of n" = n/2 seats apart
4️⃣ Fill remaining by elimination
Template (7-floor building):
Floor 7 (Top) → _____
Floor 6 → _____
Floor 5 → _____
Floor 4 → _____
Floor 3 → _____
Floor 2 → _____
Floor 1 (Ground) → _____
Common clues decoded:
"Above" = higher floor number | "Below" = lower floor number
"Immediately above" = floor n+1 | "2 floors above" = floor n+2
"As many above as below" = middle floor (n+1)/2
"Only one person between A and B" = exactly 1 floor gap
Matrix approach (best for complex puzzles):
Draw a grid: people on rows, attributes on columns. Mark ✓ for confirmed, ✗ for impossible. When a row/column has only one ✓ left — that's the answer.
Golden rules:
1️⃣ Every ✓ in a cell = ✗ for all other cells in same row AND same column
2️⃣ Work with the most constrained person/slot first
3️⃣ "If A then B" type clues — test both cases if stuck
4️⃣ Re-read the question after solving — sometimes asks "who is NOT..."
⏱️ Time target:
5-variable puzzle: 3–4 min | 6-variable: 4–5 min | 7+ variable: attempt only if easy clues visible
TCS NQT, Infosys, Wipro, Cognizant, Accenture, Capgemini, HCL, Tech Mahindra, LTI Mindtree, Mphasis, L&T Infotech, Hexaware, Persistent, Cyient, Zensar, KPIT, Birlasoft, Sonata Software, Coforge, and 30+ other service companies test these topics in campus placements.
Week 1-2: Learn blood relations, coding-decoding, syllogisms (solve 50 questions each). Week 3: Practice seating arrangement, direction sense, puzzles (30 questions each). Week 4: Take full-length mock tests (10-15 tests) and revise weak topics. Daily: 20-30 logical reasoning questions.
High-priority topics (60-70% questions): Percentages, Ratios, Time-Speed-Distance, Profit-Loss, Simple & Compound Interest. Medium-priority: Time-Work, Averages, Algebra identities. Practice 200+ questions in high-priority topics first.
Draw a family tree diagram while reading the question. Mark gender (M/F) clearly. Track generations (grandparent → parent → child). Common trick: "Only son of my father" = myself (if I'm male). Practice 50+ blood relation questions to build speed.