give me tricks to solve faster above questions with ease to understand#
Here are easy-to-understand tricks and shortcuts to solve the previously shared quantitative aptitude questions faster, grouped by topic with simple explanations and examples:
1. Number System Tricks#
- Divisibility rules help quickly find HCF/LCM, e.g., 6 divisible by 2 and 3; 15 divisible by 3 and 5, etc.
- Shortcut for LCM and HCF: Use prime factorization or the relation: $\text{LCM} \times \text{HCF} = \text{Product of two numbers}$.
2. HCF & LCM Speed Tips#
- Factorize numbers into primes quickly (2,3,5,7,11 steps).
- For multiple numbers: Take highest powers of common prime factors for LCM, and lowest powers for HCF.
- When numbers are multiples, LCM is the largest number, HCF is the smaller.
3. Ratio & Proportion Tricks#
- Add parts of the ratio for total parts.
- Share quantity proportionally: For ratio 2:3 and total 1200 → each part = 1200/5 = 240 → Multiply parts accordingly.
4. Percentages Tips#
- Express increase/decrease directly: Increase by x% → multiply by (100 + x)/100. Decrease by x% → multiply by (100 - x)/100.
- Use complements like 25% = 1/4, 50% = 1/2 to simplify calculations.
5. Average Calculation Shortcuts#
- Use total sum = average × number of values directly.
- For changing averages after an addition/removal, multiply new average by new number to find sum and subtract old sum to find value.
6. Profit & Loss Shortcuts#
- Profit % formula: $\frac{\text{Profit}}{\text{Cost Price}} \times 100$.
- To find CP when SP and profit % are given: $CP = \frac{SP \times 100}{100 + \text{Profit %}}$.
- For discount: SP = Marked Price × (100 - Discount %)/100.
7. Simple & Compound Interest Shortcuts#
- SI: Multiply principal, rate, time, divide by 100 directly.
- CI: Use formula $A = P \times (1 + \frac{R}{100})^T$. For 2 years, square the multiplier to save time.
- Approximate compound interest by finding the difference between CI and SI if needed.
8. Simplification Tips (BODMAS)#
- Always do multiplication/division before addition/subtraction.
- Handle brackets first.
- For expressions like $6 ÷ 2(1+2)$, solve inside bracket, then do division and multiplication from left to right.
9. Time & Work Tricks#
- Work done is inversely proportional to time.
- If A does work in $x$ days, daily work = $\frac{1}{x}$. For combined work, add daily works.
- To find time taken by combined workers: $ Total work / combined daily work$.
10. Time-Speed-Distance Shortcuts#
- Use formula $Speed = \frac{Distance}{Time}$.
- Convert time to hours if given in minutes.
- For relative speed in opposite directions: Add speeds; for same direction: subtract speeds.
11. Fractions & Decimals Tips#
- Convert fractions to decimals by dividing numerator by denominator mentally if easy multiples.
- Memorize common fraction-decimal equivalents (e.g., 1/4=0.25, 1/8=0.125).
- For addition/subtraction, convert to common denominator quickly.
12. Data Interpretation Tricks#
- Sum columns or rows quickly with mental math (round numbers if allowed to estimate).
- Read questions carefully: sometimes percentage or difference questions only need parts of data.
- Practice spotting trends — increasing/decreasing — to answer quickly.
General Speed-Up Tips#
- Practice mental calculations daily for multiplication/division.
- Use approximation when exact value is not needed to shortlist answers.
- Write formulas on top of your sheet for quick reference.
- Avoid re-reading questions multiple times—read carefully once.
- Use elimination technique when guessing: remove obviously wrong choices.
If you want, I can also prepare these tricks as emoji-enhanced flashcards or quiz format with step-by-step solutions for fun practice and better retention. Would you like that? 😊📚✨