Quantitative aptitude tests are a staple of many competitive exams, online assessments, and job interviews. While a solid grasp of concepts is essential, mastering a few wellchosen shortcuts can dramatically improve accuracy and speed. This page gathers some of the most useful tricks, illustrated with clear examples, so you can tackle a wide variety of problems without getting bogged down in lengthy calculations.
1. Percentage Tricks
Percentage problems often involve finding the whole from a part, the part from a whole, or the change between two numbers. The following shortcuts cut down on mental arithmetic.
1.1. Finding the Whole Quickly
If x% of a number equals A, the whole can be obtained as A 100 / x. To avoid division, rewrite the divisor as a product of easy numbers.
Whole = 48 100 / 25 = 48 4 = 192.
1.2. Percent Increase/Decrease in One Step
To add 15% to a number, multiply the number by 1.15 (or add 10% and then half of that extra 5%). Similarly, a 20% reduction is the same as multiplying by 0.8.
1.3. CrossMultiplication Shortcut for 1%
One percent of any number = the number divided by 100. For fast mental work, move the decimal two places left. Use this to derive other percentages instantly.
2. Ratio & Proportion Tricks
Ratios compare quantities, and proportion problems often ask for an unknown term when three of the four values are known. The crossmultiplication habit works, but a few additional shortcuts speed things up.
2.1. Simplify Before Solving
Always reduce the ratio to its simplest form; this prevents large numbers later.
2.2. Alligation for Mixture Problems
When mixing two solutions of different concentrations, calculate the difference between each concentration and the desired concentration. The quantities are inversely proportional to those differences.
Differences: |3040| = 10, |7040| = 30.
Ratio of 30% to 70% = 30:10 = 3:1. Hence use three parts of 30% and one part of 70%.
3. Time & Work Tricks
Timework questions revolve around the concept of work = rate time. Treat rates as fractions of a job per day, then manipulate them algebraically.
3.1. Use 1day as Common Denominator
When two workers together finish a job in d days, each workers individual time can be found by inverting the rate.
Rate of A = 1/9, combined rate = 1/6 Rate of B = 1/6 1/9 = (32)/18 = 1/18.
Hence B alone needs 18 days.
3.2. FourStep Shortcut for Multiple Workers
1 Find the least common multiple (LCM) of the individual times.
2 Convert each workers speed to units per LCM days.
3 Add the units to get total work per LCM days.
4 Divide the LCM by the total work to obtain the combined time.
Units: 60/12 =5, 60/20 =3, 60/30 =2 total =10 units per 60 days.
Combined time = 60 /10 = 6 days.
4. Algebra Shortcuts
Algebraic manipulations can be timeconsuming if you rely on long expansions. Memorise a few patterns to cut the work dramatically.
4.1. Square of a Number Ending in 5
For any twodigit number 10a+5, its square = a(a+1) followed by 25.
4.2. Difference of Squares
Formula: (x+y)(xy) = xy. Use it to avoid expanding.
= (101+99)(10199) = 2002 = 400.
4.3. Quick Factorisation of Quadratics
For ax+bx+c, when a = 1, look for two numbers whose product = c and sum = b. If a 1, use the acmethod.
ac = 18. Numbers that multiply to 18 and sum to 11 9 and 2.
Split middle term: 6x+9x+2x+3 = 3x(2x+3) + 1(2x+3) = (3x+1)(2x+3).
5. Probability Tricks
Probability problems can look intimidating, but a few guiding ideas keep them simple.
5.1. Complement Method
When the direct calculation is messy, compute the probability of the opposite event and subtract from 1.
Total =15; P(blue) =5/15 =1/3.
Desired probability = 11/3 = 2/3.
5.2. Division into Cases Shortcut
When events are mutually exclusive, add their individual probabilities. When independent, multiply.
5.3. Use Symmetry
If a problem is symmetric, the probability of each symmetric outcome is the same. This reduces counting effort.
Total distributions = 2=8. Favorable cases = {21, 12} 2 ways.
Probability = 2/8 = 1/4.
Conclusion
Even the most challenging quantitative aptitude questions become approachable when you keep a toolbox of reliable shortcuts. The key is practice: try each trick on a variety of sample problems until it feels instinctive. Over time youll notice a marked improvement in both speed and confidence, turning exams that once seemed daunting into opportunities to showcase your analytical agility.
