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📘 Lesson 4 of 4 · Mathematical Reasoning

⚡ Quantitative Aptitude

Quantitative aptitude blends arithmetic speed, estimation, and problem-solving strategy — the practical toolkit used in competitive exams and quick real-world calculations.

Course progress: 100%

01 Key Concepts

Estimation

Quickly approximating an answer using rounded numbers, useful for checking whether a more precise calculation is reasonable.

Percentage Shortcuts

Common percentages have quick mental shortcuts: 10% = divide by 10, 50% = divide by 2, 25% = divide by 4, 1% = divide by 100.

Unit Conversion Awareness

Many aptitude problems mix units (minutes vs. hours, meters vs. kilometers) — always convert to the same unit before calculating.

Breaking Numbers Apart

Splitting a calculation into easier pieces, like computing 23 x 12 as (23x10) + (23x2), speeds up mental math significantly.

Sanity 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.

02 Solved Examples

Example 1 Estimate 48 x 21 quickly using rounding.
  1. Round 48 to 50 and 21 to 20 for a quick estimate.
  2. 50 x 20 = 1000, so the actual answer should be close to 1000.
Answer: Estimated around 1000 (actual value is 1008)
Example 2 Find 15% of 200 using percentage shortcuts.
  1. Break 15% into 10% + 5%.
  2. 10% of 200 = 20. 5% is half of 10%, so 5% of 200 = 10.
  3. Add them together: 20 + 10.
Answer: 30
Example 3 A train travels 90 km in 1.5 hours. Find its speed in km/h using unit-aware division.
  1. Speed = distance / time = 90 km / 1.5 hours.
  2. Divide: 90 / 1.5.
Answer: 60 km/h

03 Practice Questions

1Estimate 32 x 9 by rounding.
Approximately 30x10=300 (actual: 288)
2Find 20% of 150 using shortcuts.
30
3Find 5% of 400 using shortcuts.
20
4A car travels 120km in 2 hours. Find its speed.
60 km/h
5Break apart 34 x 11 into easier pieces and solve.
34x10 + 34x1 = 340+34 = 374

📄 Quantitative Aptitude — Downloadable Worksheet

10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.

🗒 Cheat Sheet ⬇ Download PDF 🖥 Interactive Worksheet