Quantitative Aptitude
Syllabus Unit: General Aptitude
Why it matters
Chapter overview
GATE's quantitative aptitude questions are calculation-heavy but formula-light — number systems and simplification, percentages/ratios/averages, time-speed-distance/work, and profit-loss/interest/mensuration each rely on a small set of ratio-based shortcuts that turn a two-minute calculation into a fifteen-second one, which matters under strict exam time pressure.
1Number Systems & Simplification
Fast simplification comes from recognising structure — divisibility rules, HCF/LCM via prime factorisation, and BODMAS order — before reaching for long division.
Learning Objectives
- Apply divisibility rules for 3, 4, 8, 9 and 11 to check factors without dividing.
- Compute HCF and LCM via prime factorisation, using HCF×LCM = product of the two numbers as a shortcut/check.
- Apply BODMAS/order of operations correctly, including nested brackets and equal-precedence operators.
- Convert recurring decimals to fractions.
Key Terms
Fast simplification comes from recognising number structure instantly rather than computing from scratch — the same handful of rules cover nearly every GATE number-systems question.
Divisibility rules worth memorising
- Divisible by 3 — digit sum divisible by 3.
- Divisible by 9 — digit sum divisible by 9.
- Divisible by 4 — last two digits divisible by 4.
- Divisible by 8 — last three digits divisible by 8.
- Divisible by 11 — (sum of digits at odd positions) − (sum at even positions) is 0 or divisible by 11.
HCF and LCM by prime factorisation
Express each number as a product of primes; HCF takes the lowest power of every common prime, LCM takes the highest power of every prime appearing in either number. HCF(a,b) × LCM(a,b) = a × b — if you've found one, get the other instantly instead of refactorising.
Recurring decimals convert to fractions directly: 0.333... = 3/9 = 1/3; 0.272727... = 27/99 = 3/11.