Why Most Students Struggle with Quant Despite Knowing the Concepts
Walk into any TCS or Infosys campus placement aptitude test, and you will find students who scored well in their engineering mathematics courses sitting stuck on a time-speed-distance problem they logically know how to solve. The issue is not understanding. It is the combination of time pressure, unfamiliar problem framing, and the absence of practiced shortcuts.
Most aptitude test preparation focuses on learning concepts. But the concepts in a placement aptitude test, ratios, percentages, time and work, simple and compound interest, permutations and combinations, are concepts you already know from school. What you have not practiced is solving a specific problem type in under 45 seconds using a shortcut rather than a full algebraic derivation.
This guide covers the shortcuts and mental models that will cut your time per question on the quant section without sacrificing accuracy.
72 seconds
Average time per question available in the TCS NQT Numerical Ability section. Most candidates who fail use 2-3 minutes on quant problems they could solve in 90 seconds with shortcuts.
The Major Company Aptitude Formats You Need to Know
Time-Speed-Distance: The Shortcut Toolkit
Time-speed-distance questions appear in nearly every placement aptitude test, and they have a small set of patterns that repeat. Learn these patterns and your time on TSD drops dramatically.
Average Speed Shortcut (Two Legs at Different Speeds): When someone travels from A to B at speed X and returns from B to A at speed Y, the average speed for the full journey is NOT (X+Y)/2. It is the harmonic mean: 2XY / (X+Y).
Example: You travel to a location at 60 km/h and return at 40 km/h. Average speed = 2(60)(40)/(60+40) = 4800/100 = 48 km/h. This takes 10 seconds once memorized. Deriving it from scratch takes two minutes.
Relative Speed (Two Objects Moving): When two objects move toward each other, add their speeds. When moving in the same direction, subtract the slower from the faster. This sounds obvious but gets confused under pressure. Write it on your scratch paper at the start of the test as a reference.
Trains Crossing Platforms: Time = (Length of train + Length of platform) / Speed. When two trains cross each other: Time = (Length1 + Length2) / Relative speed. Again, memorized as a formula rather than derived each time, this is a 20-second problem.
Profit and Loss: Four Shortcuts That Cover 80% of Problems
Shortcut 1 - Successive Discounts: Two successive discounts of a% and b% give a net discount of (a + b - ab/100)%. A 20% discount followed by a 10% discount gives 20 + 10 - 200/100 = 28% net discount. Not 30%.
Shortcut 2 - Profit Percentage When CP and SP Are Known: Profit% = (SP - CP)/CP x 100. Loss% = (CP - SP)/CP x 100. Always relative to cost price. Students frequently flip this by accident under time pressure.
Shortcut 3 - Finding CP When Profit% and SP Are Given: CP = SP x 100 / (100 + Profit%). If SP is Rs. 1200 with 20% profit: CP = 1200 x 100/120 = Rs. 1000.
Shortcut 4 - Marked Price Discount Problems: If an item is marked up by M% and then discounted by D%, the net change is M - D - MD/100. A 40% markup and 25% discount gives 40 - 25 - 10 = 5% profit. Confirm with numbers for any critical answer.
Ratios and Proportions: The Fraction Substitution Method
Many ratio problems that look complicated become straightforward when you substitute the smallest possible integers. If A:B = 3:4, let A = 3 and B = 4. If A:B:C = 2:3:5 and A+B+C = 100, then A = 20, B = 30, C = 50 (each part is 100/10). This simple substitution works for the vast majority of ratio questions in placement tests and takes seconds to set up.
3x faster
Average improvement in questions attempted per section when students switch from full algebraic derivation to pattern-specific shortcuts in a structured 4-week preparation plan
Permutations and Combinations: The Framing Problem
Most students know the nPr and nCr formulas. The actual difficulty in placement tests is identifying which one applies and setting up the problem correctly, not computing the answer.
Use Permutation (nPr) when order matters: arranging books on a shelf, seating people in specific chairs, forming a password where the sequence matters.
Use Combination (nCr) when order does not matter: choosing a team, selecting items from a group, forming a committee.
The fastest way to decide: replace the items in the problem with "red ball" and "blue ball" and ask whether swapping them gives a different answer. If yes, order matters; use permutation. If no, use combination.
For complement counting questions (how many ways can X NOT happen), compute total possibilities minus the restricted cases. This is often faster than counting allowed cases directly, particularly when the restriction is on a small number of items.
Time Management Strategy During the Test
Every aptitude test has easy, medium, and hard questions mixed together. The students who score highest are not necessarily those who can solve the hardest problems; they are the ones who never get stuck and waste time on a single hard problem while leaving easy ones unattempted.
Use a two-pass strategy. First pass: spend no more than 60 seconds on any question. If it is solvable quickly, solve it. If you need more time, mark it and move on. Second pass: return to marked questions with remaining time. You will often find that your subconscious has partially worked through the problem, or that you see a faster approach on the second look.
In sections without negative marking (TCS NQT has no negative marking in the numerical section), never leave a question blank. Eliminate obviously wrong answers, guess from the remaining options, and move on. A 1-in-3 chance of being right is always better than zero.
A 4-Week Practice Plan That Works
Week 1: Topic review and shortcut memorization. One topic per day: TSD, profit-loss, ratios, percentages, time-work, P&C. Learn three shortcuts per topic and solve 20 basic practice questions to verify understanding.
Week 2: Mixed practice sets of 25 questions timed at 30 minutes. Identify which topics still cost you the most time and revisit shortcuts.
Week 3: Full mock tests using company-specific formats (TCS NQT mock, Infosys mock). Many of these are available free on IndiaBix, PrepInsta, and Infyva's placement prep section. Review every wrong answer to understand the pattern you missed, not just the calculation.
Week 4: Speed drills. Take the 10 problem types you find slowest and do 15 questions of each type in a single session, timed. The goal is to make the pattern recognition automatic so that in the test, you spend cognitive energy on the actual calculation, not on figuring out what kind of problem you are looking at.
Topics by Frequency in TCS NQT Quant Section (Historical Data)
The goal of aptitude preparation is not to become a mathematician. It is to become fast and accurate at a small set of problem types under test conditions. Treat it like a sport. Practice with time pressure from the beginning, not as an afterthought in the final week.