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Aptitude Cheat Sheet for Placement 2026

All quantitative, logical, and verbal aptitude formulas in one place — used in TCS NQT, Infosys, Wipro, Cognizant, Accenture placement tests.

100+
Formulas
3 Sections
Quant, Logical, Verbal
31+ Companies
Placement Tests

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Get all quantitative, logical & verbal formulas in one printable PDF — perfect for last-minute revision!

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📚 What's Inside This Cheat Sheet?

📊 Quantitative

Percentages, Time-Speed, Profit-Loss, SI/CI & more

🧠 Logical

Blood Relations, Syllogisms, Series & Puzzles

📝 Verbal

Grammar, RC, Vocabulary & Para-Jumbles

🎯 Extras

Memory Tricks, Quiz & 24hr Checklist

👇 Click on any section below to expand and explore!

🎯

Interactive Mistake Detector

Test yourself! Can you spot the common traps?

Question 1 of 16
Score: 0/16

If price increases by 20% and then decreases by 20%, what is the net change?

🔥 Master these 16 mistake patterns and avoid losing 15-20 easy marks in your exam!

Last 24-Hour Revision Checklist ⏰

Your final day battle plan - tick them off!

Quantitative (3 hours)

Percentages: Basic formula + successive changes + x% profit & loss pattern

⏱️ 20 min

Time-Speed-Distance: km/h ↔ m/s conversion + relative speed + train problems

⏱️ 25 min

Profit-Loss: SP/CP formulas + discount + false weight trick

⏱️ 20 min

SI/CI: Basic formulas + CI-SI difference for 2 years trick

⏱️ 20 min

Ratio-Proportion: Componendo-Dividendo + mixture rule

⏱️ 15 min

Time-Work: Combined work formula + pipes & cisterns

⏱️ 15 min

Averages: First n numbers formulas + average change tricks

⏱️ 15 min

Ages: Ratio method + before/after formula pattern

⏱️ 10 min

Practice 20 mixed questions (speed solve)

⏱️ 40 min

Logical Reasoning (2.5 hours)

Blood Relations: All relationships + gender trick + only son/daughter pattern

⏱️ 20 min

Coding-Decoding: Letter shift + opposite letter formula (27-n) + position values

⏱️ 15 min

Syllogisms: Venn diagrams + All/Some/No rules + conversion rules

⏱️ 20 min

Seating Arrangement: Linear & circular formulas + approach strategy

⏱️ 20 min

Series: Number patterns + letter patterns + skip tricks

⏱️ 15 min

Direction Sense: NEWS mnemonic + Pythagoras for distance + turn angles

⏱️ 15 min

Calendar & Clock: Odd days + clock angle formula |11M-60H|/2

⏱️ 15 min

Ranking: Total = Top + Bottom - 1 formula

⏱️ 10 min

Data Sufficiency: Option patterns + sufficiency criteria

⏱️ 15 min

Practice 15 mixed puzzles

⏱️ 25 min

Verbal Ability (2 hours)

Sentence Correction: Subject-verb agreement + common errors list

⏱️ 20 min

Reading Comprehension: Read questions first strategy + inference vs fact

⏱️ 25 min

Para-Jumbles: Opening sentence clues + transition words + concluding patterns

⏱️ 20 min

Vocabulary: Root words (bene/mal/chron) + common prefixes

⏱️ 15 min

One-Word Substitution: Top 20 commonly asked words

⏱️ 10 min

Synonyms/Antonyms: Context-based approach + elimination

⏱️ 10 min

Practice 2 RC passages + 10 sentence corrections

⏱️ 20 min

Final 3 Hours (Night Before)

✅ Review all memory tricks & mnemonics from cheat sheet

⏱️ 30 min

✅ Go through common mistakes section - mark your weak areas

⏱️ 20 min

✅ Complete one full-length mock test (exam simulation)

⏱️ 90 min

✅ Analyze mock test errors - note formula mistakes

⏱️ 20 min

✅ Quick revision: Read this entire cheat sheet once (scan mode)

⏱️ 20 min

✅ Sleep by 11 PM - fresh mind > extra revision!

⏱️ —

✅ Keep admit card, ID, stationery ready the night before

⏱️ 10 min

✅ Morning of exam: Light revision only (formulas + tricks)

⏱️ 30 min

0 / 33 Tasks Completed

0% preparation complete - keep going!

💪

🚨 CRITICAL: This checklist assumes you've already studied. Use it for REVISION, not first-time learning!

⚡ Speed Math & Vedic Shortcuts

Save 30–60 seconds per question — these tricks separate toppers from the rest

✖️ Multiply in Seconds

× 11 Trick:

25 × 11 → write 2_5, middle = 2+5 = 7 → 275

47 × 11 → 4_7, mid = 11, carry → 517

× 25 Trick:

Any number × 25 = (number × 100) ÷ 4

36 × 25 = 3600 ÷ 4 = 900

× 125 Trick:

Any number × 125 = (number × 1000) ÷ 8

48 × 125 = 48000 ÷ 8 = 6000

× 99 / × 999 Trick:

n × 99 = n × 100 − n

37 × 99 = 3700 − 37 = 3663

² Squaring Shortcuts

Numbers ending in 5:

n5² → (n × (n+1)) then append 25

35² → 3×4=12 → 1225

75² → 7×8=56 → 5625

Near 50 squaring:

(50±n)² = (25±n) | n²

47² = (25−3) | 3² = 22|09 = 2209

53² = (25+3) | 3² = 28|09 = 2809

Near 100 squaring:

(100±n)² = (100±2n) | n²

96² = (100−8) | 16 = 92|16 = 9216

104² = (100+8) | 16 = 108|16 = 10816

% Mental Calculation Table

10%÷10
20%÷5
25%÷4
50%÷2
12.5%÷8
33.3%÷3
66.6%×2÷3
75%×3÷4
37.5%×3÷8
62.5%×5÷8
87.5%×7÷8
11.1%÷9

💡 Example:

37.5% of 480 = 480 × 3 ÷ 8 = 1440 ÷ 8 = 180

÷ Divisibility Rules

÷2Last digit is even
÷3Sum of digits divisible by 3
÷4Last 2 digits divisible by 4
÷5Ends in 0 or 5
÷6Divisible by both 2 & 3
÷7Double last digit, subtract from rest. Repeat.
÷8Last 3 digits divisible by 8
÷9Sum of digits divisible by 9
÷11(Odd-position sum) − (Even-position sum) = 0 or ±11
÷13Add 4× last digit to rest. Repeat.

🎯 Sum Formulas (Memory)

First n natural numbers:

1+2+…+n = n(n+1)/2

1 to 100 = 100×101/2 = 5050

First n odd numbers:

1+3+5+…+(2n−1) = n²

First 9 odds = 9² = 81

First n even numbers:

2+4+6+…+2n = n(n+1)

First 10 evens = 10×11 = 110

First n perfect squares:

1²+2²+…+n² = n(n+1)(2n+1)/6

First n cubes:

1³+2³+…+n³ = [n(n+1)/2]²

🔢 Power & Root Table

Squares to memorise:

1²1
2²4
3²9
4²16
5²25
6²36
7²49
8²64
9²81
10²100
11²121
12²144
13²169
14²196
15²225
16²256
17²289
18²324
19²361
20²400

Cubes to memorise:

1³1
2³8
3³27
4³64
5³125
6³216
7³343
8³512
9³729
10³1000
11³1331
12³1728

√ Square roots:

√2≈1.41 | √3≈1.73 | √5≈2.24 | √6≈2.45 | √7≈2.65

⏱️ Exam Time Management Strategy

How toppers allocate time — use this as your battle plan on exam day

TCS NQT

90 min | 80 Qs

No negative marking
Quant

Attempt ALL — no penalty

30 min
26Q
Reasoning

Skip heavy puzzles, come back

28 min
24Q
Verbal

RC last, grammar first

22 min
24Q
Buffer

Review skipped questions

10 min
—

Infosys

65 min | 60 Qs

No negative marking
Quant

80 sec/question max

20 min
15Q
Puzzles

Read fully before solving

20 min
15Q
Verbal

Speed through vocabulary

18 min
20Q
Buffer

Check starred questions

7 min
—

Wipro / Cognizant

60 min | 55 Qs

0.25 mark penalty
Quant

Only attempt if >70% confident

22 min
20Q
Reasoning

Blood relations = easy marks

22 min
20Q
Verbal

Skip if unsure — -0.25!

12 min
15Q
Buffer

Final review

4 min
—

🎯 Universal Rules (Apply to ALL Exams)

The 90-Second Rule

If you haven't cracked a question in 90 seconds, mark it and move on. Return if time permits. Time lost on hard questions = easy questions left unattempted.

Elimination First

In MCQs, eliminate 2 wrong options before calculating. Often reduces to a 50-50 guess which saves 40–60 seconds vs full calculation.

Section Order Strategy

Start with your strongest section to build confidence. Save Reading Comprehension for last — it requires fresh mental energy but can be done quickly.

Negative Marking Protocol

Only guess if you can eliminate 2 options. Expected value: 3 options left = attempt (⅓ chance beats −0.25 penalty). 4 options left = skip.

Don't Re-check Easy Questions

Re-checking questions you're confident about wastes 10–15 minutes. Use that time on unattempted questions instead.

Last 5 Minutes

Stop solving new questions. Spend last 5 minutes filling in your best guess for any blank answers (on no-penalty exams) or reviewing flagged ones.

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