Master Aptitude for IT Placements
Your complete guide to cracking quantitative aptitude & logical reasoning in TCS, Infosys, Wipro, Cognizant, Accenture and more.
Aptitude is the innate or acquired ability to solve problems using logic, reasoning, and mathematical skills. In IT campus placements, aptitude tests are the first and most critical filter — companies use them to shortlist candidates before technical rounds and interviews.
In most IT companies, 60-70% of candidates are eliminated in the aptitude round alone. A strong aptitude score doesn't just get you through — it gives you confidence for the rest of the process.
What Aptitude Tests Evaluate
- Speed — Can you solve problems under time pressure? (typically 1-2 min per question)
- Accuracy — Many exams have negative marking for wrong answers
- Problem-solving approach — Can you identify patterns and pick the right method?
- Numerical reasoning — Basic to intermediate math with practical application
- Logical thinking — Pattern recognition, deduction, and analytical skills
Three Pillars of Placement Aptitude
| Pillar | Topics | Weight |
|---|---|---|
| Quantitative Aptitude | Numbers, Percentages, Profit/Loss, Time & Work, Speed, Probability, etc. | ~50-60% |
| Logical Reasoning | Coding-Decoding, Blood Relations, Seating, Puzzles, Syllogisms | ~25-30% |
| Verbal Ability | Reading Comprehension, Grammar, Vocabulary (not covered here) | ~15-20% |
The 5-Step Framework
- Options are your friend — Work backwards from answers; plug-in is faster than algebra
- Approximation wins — If choices are spread apart, round numbers and estimate
- Unit digit analysis — Eliminate options by checking only the last digit of your calculation
- Memorize key values — Squares (1-30), cubes (1-15), fraction-to-% conversions, powers of 2
- LCM method over fractions — Converts fractional work-rate problems to whole-number arithmetic
Strategy 1: Work Backward from Answer Choices
In MCQ exams, start with option B or C (middle value) and plug it into the question. This eliminates half the options instantly.
Strategy 2: Unit Digit Analysis
If answer choices have different last digits, calculate only the unit digit of the expression.
| Base ending in | Cycle of unit digits | Period |
|---|---|---|
| 2 | 2, 4, 8, 6 | 4 |
| 3 | 3, 9, 7, 1 | 4 |
| 4 | 4, 6 | 2 |
| 7 | 7, 9, 3, 1 | 4 |
| 8 | 8, 4, 2, 6 | 4 |
| 0, 1, 5, 6 | Same digit always | 1 |
| 9 | 9, 1 | 2 |
Strategy 3: Vedic Math Multiplication
For AB × 11: Write A_(A+B)_B. Carry over if sum ≥ 10.
Example: 34 × 11 = 3_(3+4)_4 = 374
Example: 85 × 11 = 8_(13)_5 = 935 (carry the 1)
For N5²: Multiply N × (N+1), append 25.
Example: 35² = 3×4 = 12, append 25 → 1225
Example: 75² = 7×8 = 56, append 25 → 5625
Let d = N − 100. Then N² = (N + d) concatenated with d² (as 2 digits).
Example: 96²: d = −4. First part: 96−4 = 92. Last: 16. Answer = 9216
Example: 104²: d = +4. First: 104+4 = 108. Last: 16. Answer = 10816
For A × B near 100: Let da = A−100, db = B−100. Result = (A+db) | (da×db)
Example: 97 × 96: da=−3, db=−4. First: 97−4=93. Last: 12. Answer = 9312
Example: 103 × 105: da=3, db=5. First: 103+5=108. Last: 15. Answer = 10815
Strategy 4: Divisibility Rules
| Divisible by | Quick Check |
|---|---|
| 2 | Last digit is even |
| 3 | Sum of digits divisible by 3 |
| 4 | Last two digits divisible by 4 |
| 5 | Last digit is 0 or 5 |
| 6 | Divisible by both 2 and 3 |
| 8 | Last three digits divisible by 8 |
| 9 | Sum of digits divisible by 9 |
| 11 | Difference of sum of alternate digits divisible by 11 |
Strategy 5: Remainder Shortcut
Example: Remainder of (17 × 23 × 49) ÷ 12:
17 mod 12 = 5, 23 mod 12 = 11, 49 mod 12 = 1
Product = 5 × 11 × 1 = 55. Then 55 mod 12 = 7
Strategy 6: Multiply/Divide by 5, 25, 50, 125
| Multiply by | Shortcut | Example |
|---|---|---|
| ×5 | ÷2, then ×10 | 48×5 = 24×10 = 240 |
| ×25 | ÷4, then ×100 | 48×25 = 12×100 = 1200 |
| ×50 | ÷2, then ×100 | 48×50 = 24×100 = 2400 |
| ×125 | ÷8, then ×1000 | 48×125 = 6×1000 = 6000 |
Key Values to Memorize
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900
1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096
| Fraction | % | Fraction | % | Fraction | % |
|---|---|---|---|---|---|
| 1/2 | 50% | 1/6 | 16.67% | 1/11 | 9.09% |
| 1/3 | 33.33% | 1/7 | 14.28% | 1/12 | 8.33% |
| 1/4 | 25% | 1/8 | 12.5% | 1/15 | 6.67% |
| 1/5 | 20% | 1/9 | 11.11% | 1/20 | 5% |
Number system questions test your understanding of LCM, HCF, divisibility, remainders, and properties of numbers. These form the foundation of all quantitative aptitude.
Key Concepts
LCM = Least Common Multiple (smallest number divisible by both)
HCF/GCD = Highest Common Factor (largest number that divides both)
- LCM of fractions: LCM of numerators / HCF of denominators
- HCF of fractions: HCF of numerators / LCM of denominators
- Co-prime numbers: HCF = 1, so LCM = product
- For 3+ numbers: Find LCM/HCF of two at a time
Example 1: LCM & HCF Application
Q: Find the smallest number which when divided by 12, 15, and 20 leaves a remainder of 5 in each case.
12 = 2² × 3
15 = 3 × 5
20 = 2² × 5
LCM = 2² × 3 × 5 = 60
Same remainder → LCM + remainder. Different remainders → LCM − (divisor − remainder) pattern.
Example 2: HCF Application
Q: Two tankers contain 850 litres and 680 litres of fuel. Find the maximum capacity of a container that can measure the fuel of both tankers exactly.
850 = 680 × 1 + 170
680 = 170 × 4 + 0
HCF = 170 litres
Percentages are the backbone of profit/loss, interest, data interpretation, and more. Mastering percentage conversions makes you fast at almost everything else.
- X% of Y = Y% of X — Pick whichever is easier! (8% of 50 = 50% of 8 = 4)
- Break it down: 17.5% = 10% + 5% + 2.5%
- If A is 25% more than B, then B is 20% less than A (reciprocal pair)
| A more than B by | B less than A by |
|---|---|
| 10% | 9.09% |
| 20% | 16.67% |
| 25% | 20% |
| 33.33% | 25% |
| 50% | 33.33% |
Example 1: Successive Percentage Change
Q: The price of a laptop increases by 20% and then decreases by 20%. What is the net percentage change?
Here a = +20, b = −20
Many students assume +20% then −20% = no change. It's always a net LOSS. Remember: increase then same decrease always gives net loss of (x²/100)%.
Example 2: Population/Increase Problem
Q: A town's population is 50,000. It increases by 10% in the first year and 20% in the second year. What is the population after 2 years?
After year 1: 50,000 × 1.10 = 55,000
After year 2: 55,000 × 1.20 = 66,000
Net% = 10 + 20 + (10×20/100) = 32%
Population = 50,000 × 1.32 = 66,000
Profit & Loss questions revolve around Cost Price (CP), Selling Price (SP), Marked Price (MP), and discounts. Very frequently asked in TCS and Cognizant.
- CP of X items = SP of Y items: Profit% = [(X−Y)/Y] × 100
- False weight: Profit% = [(True − False) / False] × 100
- Two successive discounts d1% and d2%: Equivalent = d1 + d2 − (d1×d2/100)
Example 1: Markup & Discount
Q: A shopkeeper marks up the price of an article by 40% and then offers a 10% discount. Find his profit percentage.
Example 2: CP of X = SP of Y
Q: The cost price of 25 articles is equal to the selling price of 20 articles. Find the profit percentage.
Interest problems appear in almost every placement exam. The key is knowing when to use SI vs CI formulas and the shortcuts that save time.
- Rule of 72: Money doubles in 72/R years at compound interest
- Rule of 114: Money triples in 114/R years
- At 10% CI for 2 years: Effective rate = 21% (not 20%)
- Difference between CI and SI for 2 years: CI − SI = P(R/100)²
Example 1: Rule of 72
Q: At what rate of compound interest will Rs. 10,000 double itself in approximately 6 years?
8% → 9 years | 10% → 7.2 years | 12% → 6 years | 15% → 4.8 years
Example 2: CI vs SI Difference
Q: The difference between CI and SI on a sum of money at 10% per annum for 2 years is Rs. 50. Find the sum.
Time & Work is one of the most frequently asked topics. The LCM method is a game-changer — it eliminates fractions and makes problems incredibly fast to solve.
Instead of dealing with fractions, take the LCM of all given days as the total units of work. Then each person's daily work becomes a whole number.
- Find LCM of all the time periods
- Divide LCM by each person's days = their daily work rate (in units)
- Add/subtract rates as needed
- Time = Total units / Combined rate
Example 1: LCM Method
Q: A can complete a work in 12 days, B in 15 days, and C in 20 days. If all three work together, in how many days will the work be completed?
B's rate = 60/15 = 4 units/day
C's rate = 60/20 = 3 units/day
Notice how the LCM method converted everything to whole numbers. No messy 1/12 + 1/15 + 1/20 calculations needed!
Example 2: Work & Leaving
Q: A can do a piece of work in 10 days, B in 15 days. They work together for 4 days, then A leaves. How many more days will B take to finish the remaining work?
Speed-distance problems are about applying the basic relationship D = S × T in clever ways. The average speed trap catches most students.
- Average speed for equal distances is the HARMONIC mean, not arithmetic mean
- If speed ratio = a:b, time ratio for same distance = b:a
- Relative speed — Same direction: subtract. Opposite direction: add.
| km/hr | m/s |
|---|---|
| 36 | 10 |
| 54 | 15 |
| 72 | 20 |
| 90 | 25 |
Example 1: Average Speed Trap
Q: A person goes from A to B at 40 km/hr and returns at 60 km/hr. Find the average speed for the entire journey.
The answer is NOT 50 km/hr (which is the arithmetic mean). For equal distances, always use the harmonic mean.
Example 2: Relative Speed
Q: Two people start from two points 120 km apart and walk towards each other at 8 km/hr and 7 km/hr. After how many hours will they meet?
Train problems are a special case of speed-distance where the length of the train adds to the distance. Remember: a train has to cover its own length to completely pass something.
| Scenario | Distance to Cover | Speed |
|---|---|---|
| Train passes a pole/person | Length of train | Speed of train |
| Train passes a platform/bridge | Ltrain + Lplatform | Speed of train |
| Two trains, opposite direction | L1 + L2 | S1 + S2 |
| Two trains, same direction | L1 + L2 | S1 − S2 |
Example 1: Train & Platform
Q: A train 200m long runs at 72 km/hr. How long does it take to cross a 300m platform?
Example 2: Two Trains Opposite Direction
Q: Two trains of lengths 150m and 250m are moving in opposite directions at 54 km/hr and 36 km/hr. How long to cross each other?
Pipes & Cisterns is essentially Time & Work with one twist: leaks do negative work. Use the same LCM method!
Filling pipe = positive work. Emptying pipe/leak = negative work.
Example 1: Three Pipes
Q: Pipe A fills a tank in 12 hours, B fills in 15 hours, C empties in 20 hours. If all three are open, how long to fill the tank?
Example 2: Leak Problem
Q: A pipe can fill a tank in 6 hours. Due to a leak, it takes 8 hours. How long will the leak take to empty a full tank?
Average questions often appear in combination with data interpretation. The deviation method lets you calculate averages mentally.
Pick an assumed mean 'A' near the values. Average = A + (sum of deviations / n).
Example: Average of 48, 52, 55, 47, 53. Assume A = 50.
Deviations: −2, +2, +5, −3, +3 = +5. Average = 50 + 5/5 = 51
Example 1: Replacement
Q: The average age of 30 students is 15 years. If the teacher's age is included, the average increases by 1. What is the teacher's age?
Example 2: Batsman's Average
Q: A batsman has an average of 40 runs in 9 innings. How many runs must he score in the 10th innings to raise his average to 42?
Runs needed = New average + (Number of previous innings × increase) = 42 + 9×2 = 60
Ratios underpin many other topics (mixtures, ages, work). Mastering ratio manipulation is essential for speed.
Example 1: Proportional Division
Q: Divide Rs. 3,600 among A, B, C in the ratio 2:3:4.
Example 2: Combining Ratios
Q: If A:B = 2:3 and B:C = 4:5, find A:B:C.
The Alligation (Cross) method is one of the most powerful shortcuts in aptitude. It works for mixing solutions, combining groups, and even average speed problems!
To find the ratio of mixing two ingredients at concentrations (or prices) C1 and C2 to get a mean Cm:
Works for prices, concentrations, averages, speeds — anything where you mix two groups!
Remaining = V × (1 − X/V)N
Example 1: Alligation
Q: In what ratio must rice at Rs. 30/kg be mixed with rice at Rs. 42/kg to get a mixture worth Rs. 34/kg?
Example 2: Repeated Dilution
Q: A vessel contains 20L of milk. 4L is removed and replaced with water. This is done 3 times. How much milk remains?
Age problems always reduce to simple linear equations. The key insight: the difference of ages remains constant regardless of time.
Age difference never changes. If father is 30 years older than son today, he'll be 30 years older forever. Use this to set up equations quickly.
Example 1: Ratio of Ages
Q: The ages of A and B are in the ratio 3:5. After 4 years, their ratio becomes 2:3. Find their present ages.
Example 2: Years Ago Problem
Q: 5 years ago, a father was 7 times as old as his son. 5 years from now, the father will be 3 times as old as the son. Find their current ages.
Permutation = arrangement (order matters). Combination = selection (order doesn't matter). The key is identifying which one the question needs.
- "How many ways to arrange?" → Permutation
- "How many ways to select/choose?" → Combination
- "At least one" → Total − None (complementary counting)
| n | nC2 | nC3 |
|---|---|---|
| 5 | 10 | 10 |
| 6 | 15 | 20 |
| 7 | 21 | 35 |
| 8 | 28 | 56 |
| 10 | 45 | 120 |
| 12 | 66 | 220 |
Example 1: Committee Formation
Q: From a group of 6 men and 4 women, a committee of 5 is to be formed with at least 2 women. How many ways?
2W + 3M, or 3W + 2M, or 4W + 1M
4C3 × 6C2 = 4 × 15 = 60
4C4 × 6C1 = 1 × 6 = 6
Example 2: Word Arrangement
Q: How many different words can be formed from the letters of "MISSISSIPPI"?
Probability measures the chance of an event occurring (0 to 1). The #1 shortcut: for "at least one" questions, ALWAYS use 1 − P(none).
| Scenario | Probability |
|---|---|
| Sum of 7 with two dice | 6/36 = 1/6 (most likely sum) |
| Getting a doublet | 6/36 = 1/6 |
| Drawing an ace from 52 cards | 4/52 = 1/13 |
| Drawing a face card | 12/52 = 3/13 |
Example 1: At Least One (Complementary)
Q: A coin is tossed 4 times. What is the probability of getting at least one head?
Example 2: Cards
Q: Two cards are drawn from a standard 52-card deck. What is the probability that both are aces?
Number series tests pattern recognition. The trick is having a systematic approach rather than guessing randomly.
- Differences: Write differences between consecutive terms
- Second differences: If first differences aren't obvious, take differences of differences
- Ratios: Check if consecutive terms have a common ratio
- Alternating: Check odd-position and even-position terms separately
- Known sequences: Squares, cubes, primes, triangular numbers, Fibonacci
| Type | Sequence |
|---|---|
| Triangular | 1, 3, 6, 10, 15, 21, 28, 36, 45, 55... |
| Fibonacci | 1, 1, 2, 3, 5, 8, 13, 21, 34, 55... |
| Primes | 2, 3, 5, 7, 11, 13, 17, 19, 23, 29... |
| n² + 1 | 2, 5, 10, 17, 26, 37, 50... |
| n³ | 1, 8, 27, 64, 125, 216, 343... |
Example 1: Difference Pattern
Q: Find the next number: 2, 5, 10, 17, 26, ?
Example 2: Alternating Series
Q: Find the next number: 3, 8, 6, 14, 12, 20, ?
Odd positions: 3, 6, 12 → each ×2!
Even positions: 8, 14, 20 → +6 each time
Logarithm questions test your knowledge of properties. Memorize the rules and common log values, and most problems become straightforward.
| Property | Formula |
|---|---|
| Product Rule | log(ab) = log a + log b |
| Quotient Rule | log(a/b) = log a − log b |
| Power Rule | log(an) = n · log a |
| Base Change | logab = log b / log a = 1/logba |
| Identity | logaa = 1 |
| Log of 1 | loga1 = 0 |
log10 2 = 0.3010 | log10 3 = 0.4771 | log10 5 = 0.6990 | log10 7 = 0.8451
Useful: Number of digits in N = floor(log10 N) + 1
log(a + b) ≠ log a + log b. There is NO shortcut for log of a sum!
Example 1: Simplification
Q: Find the value of log28 + log381 − log525
Example 2: Number of Digits
Q: How many digits are there in 250? (Given: log 2 = 0.3010)
Exponent rules and rationalization are the two pillars here. Questions are typically about simplification and comparison.
| Rule | Formula |
|---|---|
| Multiplication | am × an = am+n |
| Division | am / an = am−n |
| Power of power | (am)n = amn |
| Zero exponent | a0 = 1 |
| Negative | a−n = 1/an |
| Fractional | am/n = n√(am) |
Tip: Multiply by the conjugate to remove surds from the denominator.
Useful values: √2 = 1.414 | √3 = 1.732 | √5 = 2.236 | √7 = 2.646
Example 1: Simplification
Q: Simplify: (27)2/3 × (8)−1/3
Example 2: Comparing Surds
Q: Which is greater: √3 or ³√4?
Calendar problems use the "odd days" method. Once you memorize the odd-day counts, finding the day of any date becomes mechanical.
| Period | Odd Days |
|---|---|
| Ordinary year (365 days) | 1 |
| Leap year (366 days) | 2 |
| 100 years | 5 |
| 200 years | 3 |
| 300 years | 1 |
| 400 years | 0 |
Day codes: 0=Sun, 1=Mon, 2=Tue, 3=Wed, 4=Thu, 5=Fri, 6=Sat
Month odd days: Jan=3, Feb=0(1 leap), Mar=3, Apr=2, May=3, Jun=2, Jul=3, Aug=3, Sep=2, Oct=3, Nov=2, Dec=3
- Divisible by 4 → Leap year
- Divisible by 100 → NOT a leap year
- Divisible by 400 → IS a leap year
- Examples: 2000 (leap), 1900 (not leap), 2024 (leap)
Example 1: Find the Day
Q: What day of the week was 15th August 1947?
1600 years = 0 odd days
300 years = 1 odd day
46 years = 11 leap + 35 ordinary = 22 + 35 = 57 odd days. 57 mod 7 = 1
Total from years = 0 + 1 + 1 = 2
3 + 0 + 3 + 2 + 3 + 2 + 3 = 16. 16 mod 7 = 2
Example 2: Next Year's Day
Q: If January 1, 2023 is a Sunday, what day is January 1, 2024?
Ordinary year: next year's same date = +1 day. Leap year: +2 days.
All clock problems can be solved with one magic formula. Memorize it and you'll never struggle with clock angles again.
Where H = hour, M = minutes. If result > 180°, subtract from 360°.
- Hands overlap 11 times in 12 hours (every 65.45 minutes)
- Hands are at right angles (90°) 22 times in 12 hours
- Hands are in straight line (180°) 11 times in 12 hours
- Minute hand gains 5.5 degrees per minute over the hour hand
Example 1: Find the Angle
Q: What is the angle between the hour and minute hand at 3:20?
Example 2: When Do Hands Overlap?
Q: At what time between 4 and 5 o'clock do the hour and minute hands overlap?
Simplification tests your ability to solve complex arithmetic expressions quickly using BODMAS and estimation. Approximation is about finding near-accurate answers rapidly when exact calculation is time-consuming.
- Round to nearest 10: 49.8 ≈ 50, 101.3 ≈ 100. Adjust the error at the end.
- Fraction trick: 999 ÷ 7 ≈ 1000 ÷ 7 ≈ 142.8 (close enough for MCQs)
- Square root approx: √50 is between √49=7 and √64=8, closer to 7, so ≈7.07
- Percentage to decimal: Instantly convert for multiplication — 37.5% = 0.375
Example 1: BODMAS Application
Q: Simplify: 36 ÷ 4 + 3 × 2 − (8 − 3)
Example 2: Approximation
Q: Find the approximate value of: 4999 ÷ 49.8 + 201.3 × 9.9
Example 3: Algebraic Identity Shortcut
Q: Find: (478)² − (322)²
Never try to compute 478² and 322² separately — it wastes time and invites errors. Always check for algebraic identities first.
In approximation questions, check how spread apart the answer options are. If options are 2000, 2100, 2200, 2300 — rough rounding works. If options are 2093, 2097, 2101, 2107 — you need more precision.
Partnership questions deal with sharing profits (or losses) among business partners based on their capital investment and the duration for which they invested.
- Equal time: Profit ratio = Capital ratio directly
- Equal capital: Profit ratio = Time ratio directly
- Working partner bonus: Deduct the salary/bonus first, then divide remaining profit in ratio
Example 1: Simple Partnership
Q: A and B invest Rs. 40,000 and Rs. 60,000 respectively. If the total profit is Rs. 25,000, find A's share.
Example 2: Varying Investment Periods
Q: A invests Rs. 30,000 for 12 months. B invests Rs. 45,000 for 8 months. Profit is Rs. 18,000. Find B's share.
Example 3: Working Partner Salary
Q: A and B invest Rs. 50,000 and Rs. 30,000 respectively. A manages the business and gets 10% of profit as salary. Remaining profit is split in capital ratio. Total profit is Rs. 40,000. Find A's total earnings.
Boats & Streams is a special case of speed problems where the water current aids or opposes the boat's motion. Master the 4 key formulas and these become easy marks.
- If time taken is same upstream and downstream: Distance ratio = Speed ratio (downstream : upstream)
- Round trip (same distance): Average speed = (u² − v²) / u, where u = boat speed, v = stream speed
- Still water questions: Stream speed = 0, so just use Distance = Speed × Time
Example 1: Finding Speed
Q: A boat goes 20 km downstream in 2 hours and returns in 4 hours. Find the speed of the boat in still water and the speed of the stream.
Example 2: Distance Covered
Q: A man can row at 8 km/hr in still water. If the river flows at 2 km/hr, how long will he take to row 30 km upstream and return?
Example 3: Stream Speed From Round Trip
Q: A boat takes 6 hours to travel 36 km downstream and 36 km upstream. If the boat speed in still water is 9 km/hr, find the stream speed.
Always check that your numbers give a valid equation. If you get a negative under the square root or impossible time, recheck the question setup.
Data Interpretation (DI) questions present data in tables, charts, or graphs. You must extract, calculate, and compare values. Speed and approximation skills are critical here.
- Bar chart: Estimate bar heights visually before calculating — eliminates 2 options instantly
- Pie chart: 1% of 360° = 3.6°. So 25% = 90°, 50% = 180°
- Line graph: Steepest slope = highest growth rate. Flat = no change.
- Caselet: Draw a rough table from the text data before solving
Use this data for Examples 1-3:
| Department | 2022 Revenue (Lakhs) | 2023 Revenue (Lakhs) | Employees |
|---|---|---|---|
| Sales | 120 | 150 | 40 |
| IT | 200 | 240 | 60 |
| HR | 80 | 72 | 20 |
| Marketing | 100 | 130 | 30 |
| Total | 500 | 592 | 150 |
Example 1: Percentage Share
Q: What percentage of total 2023 revenue comes from IT?
Example 2: Growth Rate
Q: Which department had the highest growth rate from 2022 to 2023?
Example 3: Revenue Per Employee
Q: Which department has the highest revenue per employee in 2023? What is the ratio of highest to lowest?
In DI, speed is everything. Don't calculate exact values unless the options are very close. Use approximation first, then refine only if needed. Also, read ALL questions for a data set before starting — later questions sometimes reveal patterns useful for earlier ones.
Coding-Decoding tests pattern recognition. You're given a rule that transforms one word/number into another and must apply the same rule.
- Letter shifting: Each letter moves forward/backward by a fixed number (A+2=C, B+2=D...)
- Reverse order: WORD becomes DROW
- Position-based: Letter number in alphabet (A=1, B=2, ... Z=26)
- Mirror coding: A↔Z, B↔Y, C↔X (position sums to 27)
- Number substitution: Each letter replaced by its position number
- Vowel/consonant based: Different rules for vowels vs consonants
Example 1: Letter Shifting
Q: If COMPUTER is coded as DPNQVUFS, how is LAPTOP coded?
Example 2: Mirror Coding
Q: In a code, APPLE is written as ZKKOV. How is MANGO written?
Blood relation problems test your ability to trace family connections. Drawing a family tree is the most reliable approach.
| Relation | Meaning |
|---|---|
| Father's/Mother's son | Brother |
| Father's/Mother's daughter | Sister |
| Father's brother | Uncle (Paternal) |
| Mother's brother | Uncle (Maternal) |
| Father's/Mother's father | Grandfather |
| Son's wife | Daughter-in-law |
| Daughter's husband | Son-in-law |
| Brother's/Sister's son | Nephew |
| Brother's/Sister's daughter | Niece |
Key tip: Always draw the family tree! Use arrows for parent-child and lines for siblings/spouse.
Example 1
Q: Pointing to a photograph, Arun says "She is the daughter of my grandfather's only son." How is the girl related to Arun?
Example 2
Q: A is the mother of B. B is the sister of C. D is the son of C. E is the brother of D. How is A related to E?
Seating and direction problems require spatial visualization. Draw diagrams — always!
Remember: North(up), East(right), South(down), West(left).
- Turn right from North = East
- Turn left from North = West
- Opposite of North-East = South-West
- Pythagoras: Final distance = √(horizontal² + vertical²)
- Facing center: Right of person = your left when looking at diagram
- Facing outside: Everything reverses
- Start with the most constrained clue first
- Use definite clues before relative ones
Example 1: Direction
Q: A man walks 3 km North, turns right and walks 4 km, then turns right and walks 3 km. How far is he from the starting point?
Example 2: Linear Seating
Q: Five people A, B, C, D, E sit in a row facing north. B sits to the right of A. D sits at the extreme right. C sits between A and D. Who sits in the middle?
Syllogisms are logical arguments where conclusions are drawn from two or more premises. You must determine if a conclusion logically follows from the given statements, regardless of real-world truth. Use Venn diagrams to solve.
| Statement | Venn Diagram | Converse |
|---|---|---|
| All A are B | A circle completely inside B | Some B are A (valid) |
| No A are B | A and B don't overlap | No B are A (valid) |
| Some A are B | A and B partially overlap | Some B are A (valid) |
| Some A are not B | Part of A is outside B | No valid converse |
- "All A are B" does NOT mean "All B are A"
- "All A are B" DOES imply "Some A are B" and "Some B are A"
- "No A are B" = "No B are A" (fully reversible)
- A conclusion follows ONLY if it is true in ALL possible valid Venn diagrams
- "Either I or II follows" when I and II are complementary (one must be true)
Example 1: All-All Chain
Q: Statements: All dogs are animals. All animals are living beings. Conclusions: (I) All dogs are living beings. (II) Some living beings are dogs.
Example 2: Some-No Combination
Q: Statements: Some cats are dogs. No dogs are birds. Conclusions: (I) No cats are birds. (II) Some cats are not birds.
Example 3: Complementary Pair
Q: Statements: All pens are books. Some books are erasers. Conclusions: (I) All erasers are pens. (II) Some erasers are not pens.
When neither conclusion follows individually, check if they form a complementary pair (All vs Some...not). If yes, "Either I or II follows" is the answer.
Puzzle questions give a set of conditions about arrangements (seating, floors, scheduling) and ask you to deduce the complete arrangement. These are time-consuming but high-scoring if solved correctly.
- Read ALL clues first before placing anyone
- Start with definite clues (e.g., "A sits at the left end")
- Use elimination: If A can't be in positions 2 or 3, and position 1 is taken, A must be in 4 or 5
- Try case analysis: If stuck, assume two possible cases and test each against remaining clues
- Verify: After completing, check ALL conditions once more
Example 1: Linear Arrangement
Q: Five friends P, Q, R, S, T sit in a row facing North. R is in the middle. P is to the immediate left of R. T is at the right end. Who is between Q and T?
Example 2: Circular Arrangement
Q: Six people A, B, C, D, E, F sit around a circular table facing the center. A is opposite D. B is to the immediate right of A. C is not adjacent to D. Where does F sit?
Example 3: Floor Arrangement
Q: 5 people (A-E) live on floors 1-5 (ground=1, top=5). B lives above A. C lives on floor 3. D lives immediately below E. A does not live on floor 1. Find the arrangement.
Data Sufficiency tests whether the given statements provide enough information to answer a question. You don't need to solve the problem — just determine if it CAN be solved. This is a favourite in Morgan Stanley and CAT exams.
| Choice | Meaning |
|---|---|
| (A) | Statement I alone is sufficient |
| (B) | Statement II alone is sufficient |
| (C) | Both together are sufficient, but neither alone |
| (D) | Each alone is sufficient |
| (E) | Neither alone nor together is sufficient |
- Step 1: Consider Statement I alone. Can you answer? If yes, eliminate B, C, E.
- Step 2: Consider Statement II alone (forget Statement I). Can you answer? If yes, eliminate A, C, E.
- Step 3: If neither alone works, combine them. If combined works → C. If not → E.
- Don't solve: Just determine sufficiency. Saves time.
Example 1: Statement I Sufficient
Q: What is the value of x? (I) x + 5 = 12. (II) x is a prime number less than 10.
Example 2: Both Together Needed
Q: Is x > y? (I) x = 2y − 3. (II) y = 5.
Example 3: Neither Sufficient
Q: What is the area of triangle ABC? (I) AB = 10 cm. (II) Angle A = 60°.
Don't assume a triangle is equilateral, right-angled, or isosceles unless explicitly stated. With one side and one angle, infinite triangles are possible.
Input-Output questions show a "machine" that rearranges numbers or words in each step following a hidden rule. You must discover the rule and predict intermediate or final steps.
- Compare Input with Step 1: What changed? Which element moved? Where did it go?
- Compare Step 1 with Step 2: Same rule or different?
- Common patterns: Sorting (ascending/descending), alternating smallest/largest to ends, alphabetical rearrangement
- Track one element: Follow where a single number/word moves across steps
Example 1: Number Sorting
Q: Input: 45 12 78 33 9 56. Step 1: 9 45 12 78 33 56. Step 2: 9 12 45 78 33 56. Step 3: 9 12 33 45 78 56. Step 4: 9 12 33 45 56 78. What is the rule?
Example 2: Word Rearrangement
Q: Input: go set map bit ace top. Step 1: ace go set map bit top. Step 2: ace bit go set map top. Step 3: ace bit go map set top. What is Step 4?
Example 3: Alternating Pattern
Q: Input: 14 7 32 19 5 28. Step 1: 5 14 7 32 19 28. Step 2: 5 14 7 19 28 32. Step 3: 5 7 14 19 28 32. What is the pattern?
Don't assume simple ascending/descending sort. Many input-output machines alternate between picking smallest and largest, or sort words and numbers by different rules simultaneously.
Quick-reference card of the most important formulas. Bookmark this for last-minute revision!
| Topic | Key Formula |
|---|---|
| LCM & HCF | LCM × HCF = a × b |
| Percentages | Successive: a + b + ab/100 |
| Profit & Loss | Net P% = Markup% − Discount% − (M×D/100) |
| Simple Interest | SI = PRT/100 |
| Compound Interest | A = P(1+R/100)T |
| CI − SI (2 yrs) | P(R/100)² |
| Rule of 72 | Doubling time = 72/R |
| Time & Work | Together = ab/(a+b) days |
| Average Speed | 2ab/(a+b) for equal distances |
| Trains | Time = Total length / Relative speed |
| Pipes (leak) | Leak time = ab/(b−a) |
| Alligation | Ratio = |C2−Cm| : |Cm−C1| |
| Repeated Dilution | V(1 − X/V)N |
| Clock Angle | |30H − 11M/2| |
| Calendar | Ordinary year = 1 odd day, Leap = 2 |
| Probability | P(at least 1) = 1 − P(none) |
| P & C | nCr = n!/[r!(n−r)!] |
| Logarithm | log(an) = n.log(a) |
| Boats & Streams | Still water speed = (D+U)/2, Stream = (D−U)/2 |
| Partnership | Profit ratio = CapitalA×TimeA : CapitalB×TimeB |
| Simplification | a²−b² = (a+b)(a−b) |
Different companies emphasize different topics. Here's what to prioritize based on your target company.
| Company | Exam Name | High-Priority Topics | Tips |
|---|---|---|---|
| TCS | TCS NQT | Number Series, Percentages, P&L, Time & Work, Probability, Clocks, Calendar | Moderate difficulty. Focus on speed. ~25-30 questions in 40 min. |
| Infosys | InfyTQ | Percentages, Profit/Loss, Time-Speed-Distance, P&C, Probability, Logarithms | Slightly harder math. Practice DI sets. |
| Wipro | NLTH | Time & Work, Speed & Distance, Averages, Blood Relations, Coding-Decoding | Mix of quant + logical. Medium difficulty. |
| Cognizant | GenC / GenC Next | Number Systems, Percentages, P&L, Ratio, Averages, Seating | GenC is easier than GenC Next. Focus on fundamentals. |
| Accenture | Accenture Assessment | Percentages, Profit/Loss, Time & Work, Ages, Blood Relations | Relatively easier. Speed is key — lots of questions, less time. |
| Capgemini | Game-based | Logical Reasoning, Number Series, Coding, Spatial Reasoning | Unique game-based format. Practice spatial & pattern games. |
| Morgan Stanley | Online Assessment + Interviews | Probability, P&C, Puzzles, Number Theory, Data Interpretation, Logical Reasoning, Mental Ability | High difficulty. Strong focus on quant & puzzles. Expect brain-teasers in interviews. See detailed breakdown below. |
| Deloitte | Deloitte Assessment | Quantitative Aptitude, Logical Reasoning, Verbal Ability, Business Scenarios | Moderate difficulty. Strong verbal section. Case-study based DI sets. |
| Goldman Sachs | HackerRank + Interviews | Probability, P&C, Number Theory, Puzzles, Data Structures, Algorithms | Very high difficulty. Focus on mathematical reasoning and coding. Expect brain-teasers. |
| Amazon | Online Assessment | Logical Reasoning, Data Interpretation, Coding (2-3 problems), Work Simulation | Heavy coding focus. Aptitude is secondary but still tested. Leadership principles matter in interviews. |
Morgan Stanley — Detailed Exam Pattern
Morgan Stanley is one of the most sought-after companies in campus placements, especially for technology and finance roles. Their selection process is rigorous and consists of multiple rounds designed to test mathematical aptitude, logical thinking, coding ability, and domain knowledge.
Selection Process Overview
| Round | Format | Duration | Details |
|---|---|---|---|
| Round 1: Online Assessment | MCQ + Coding | 90–120 minutes | Aptitude (Quant + Logical) + 2–3 coding problems. Conducted on HackerRank or similar platforms. |
| Round 2: Technical Interview 1 | Face-to-face / Virtual | 45–60 minutes | DSA, OOP concepts, DBMS, OS. May include live coding on a whiteboard. |
| Round 3: Technical Interview 2 | Face-to-face / Virtual | 45–60 minutes | Advanced problem-solving, system design (for experienced roles), puzzles, and brain-teasers. |
| Round 4: HR / Managerial Round | Discussion | 30–45 minutes | Behavioural questions, situational judgement, "Why Morgan Stanley?", strengths/weaknesses. |
Online Assessment — Aptitude Section Breakdown
| Topic Area | Weightage | Difficulty | Key Sub-topics |
|---|---|---|---|
| Quantitative Aptitude | ~40% | High | Probability, P&C, Number Theory (divisibility, remainders, modular arithmetic), Algebra, Percentages, Ratio & Proportion, SI/CI |
| Logical Reasoning | ~25% | Medium–High | Puzzles (seating, scheduling), Syllogisms, Data Sufficiency, Blood Relations, Coding-Decoding |
| Data Interpretation | ~15% | Medium–High | Tables, Bar/Line/Pie charts, Caselets. Requires quick calculation and approximation. |
| Verbal Ability | ~10% | Medium | Reading Comprehension, Sentence Correction, Para Jumbles |
| Coding | ~10% (separate) | Medium–High | 2–3 coding questions (arrays, strings, DP, graphs). Languages: C++, Java, Python. |
Morgan Stanley — Most Frequently Asked Aptitude Topics
- Probability & P&C: Conditional probability, Bayes' theorem, dice/cards/balls problems, arrangement with restrictions. This is their #1 favourite topic.
- Number Theory: GCD/LCM, modular arithmetic, last digits of large powers, divisibility rules for large numbers, prime factorisation.
- Puzzles & Brain-Teasers: Classic puzzles like the "100 locker problem," "weighing 8 balls to find the heavier one," "crossing a bridge in minimum time." Expected in interviews, not just the written test.
- Data Interpretation: Complex multi-graph DI sets with 4–5 questions each. Requires speed and approximation skills.
- Time, Speed & Distance: Relative motion, trains, boats & streams, circular track meetings.
- Profit & Loss / Percentages: Multi-step problems involving successive discounts, marked price chains, partnerships.
Sample Morgan Stanley-Level Questions
A bag contains 5 red, 4 blue, and 3 green balls. Three balls are drawn at random. What is the probability that exactly 2 are red?
Solution:
Total ways to pick 3 from 12 = 12C3 = 220
Ways to pick 2 red from 5 = 5C2 = 10
Ways to pick 1 non-red from 7 = 7C1 = 7
Favorable = 10 × 7 = 70
P = 70 / 220 = 7/22
What is the remainder when 2^256 is divided by 17?
Solution (using Fermat's Little Theorem):
Since 17 is prime and gcd(2, 17) = 1, by Fermat's Little Theorem: 2^16 ≡ 1 (mod 17)
256 = 16 × 16, so 2^256 = (2^16)^16 ≡ 1^16 ≡ 1 (mod 17)
Remainder = 1
You have 8 identical-looking balls. One is heavier than the rest. Using a balance scale, what is the minimum number of weighings needed to find the heavier ball?
Solution:
Divide into 3 groups: 3, 3, 2.
Weighing 1: Compare the two groups of 3.
- If one side is heavier → the heavy ball is in that group of 3.
- If balanced → the heavy ball is in the remaining group of 2.
Weighing 2:
- If group of 3: weigh 1 vs 1 from that group. If balanced, the third is heavy. If not, the heavier side is the answer.
- If group of 2: weigh 1 vs 1. The heavier one is the answer.
Answer: 2 weighings
- Probability is king: Spend extra time mastering conditional probability, Bayes' theorem, and combinatorics. At least 30% of their quant section involves these topics.
- Practice puzzles separately: Keep a list of 50+ classic interview puzzles. Morgan Stanley interviewers love them, especially for technology roles.
- Speed matters: The online test is time-pressured. Practice DI sets under timed conditions — aim for 2–3 minutes per DI question.
- Don't ignore coding: Even if you're preparing for aptitude, the coding section is a hard filter. Practice medium-level LeetCode problems (arrays, strings, DP).
- Brush up mental math: Morgan Stanley questions often involve large numbers. Knowing squares up to 30, cubes up to 15, and fraction-percentage conversions is essential.
- Expect the unexpected: Interview questions can be open-ended ("How many tennis balls fit in this room?"). These test structured thinking, not exact answers.
- Week 1-2: Master basics — Percentages, Ratio, Averages, Number Systems
- Week 3-4: Core problem-solving — Time & Work, Speed & Distance, P&L, Interest
- Week 5-6: Advanced topics — P&C, Probability, Series, Logarithms
- Week 7-8: Logical Reasoning & Mock Tests. Take at least 10 full-length mocks.
Daily practice: Solve 20-30 problems. Time yourself. Review mistakes. Repeat.