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Mathematical Reasoning · Quick Reference
Quantitative Aptitude Cheat Sheet
In one line: quantitative aptitude blends arithmetic speed, estimation, and problem-solving strategy — the practical toolkit used in competitive exams and quick real-world calculations.
Key Ideas
1Estimation. Quickly approximating an answer using rounded numbers, useful for checking whether a more precise calculation is reasonable.
2Percentage Shortcuts. Common percentages have quick mental shortcuts: 10% = divide by 10, 50% = divide by 2, 25% = divide by 4, 1% = divide by 100.
3Unit Conversion Awareness. Many aptitude problems mix units (minutes vs. hours, meters vs. kilometers) — always convert to the same unit before calculating.
4Breaking Numbers Apart. Splitting a calculation into easier pieces, like computing 23 x 12 as (23x10) + (23x2), speeds up mental math significantly.
5Sanity Checking Answers. After calculating, briefly ask whether the answer's size and sign make sense given the context of the problem — a quick way to catch careless errors.
Worked Examples
Estimate 48 x 21 quickly using rounding.
Estimated around 1000 (actual value is 1008)
Find 15% of 200 using percentage shortcuts.
30
A train travels 90 km in 1.5 hours. Find its speed in km/h using unit-aware division.
60 km/h
Practice Yourself
Estimate 32 x 9 by rounding.
Approximately 30x10=300 (actual: 288)
Find 20% of 150 using shortcuts.
30
Find 5% of 400 using shortcuts.
20
A car travels 120km in 2 hours. Find its speed.
60 km/h