Key takeaways
- Shortcuts work only when you know why they work. Learn the idea, then the shortcut.
- Fractions, ratios and multipliers handle most percentage, profit and interest questions faster than long arithmetic.
- Estimation and options help you eliminate wrong answers in multiple choice questions.
- Practise each shortcut on ten questions before trusting it in a mock.
Arithmetic carries a large share of CAT Quant, and the questions are designed so that long calculation is slower than a good shortcut. These are the methods that save the most time, with the reasoning behind each so that you can adapt them to new questions. They are covered with practice questions on our CAT topic pages.
1. Use fractions for common percentages
Learn the fraction for the percentages that appear most often: 50% is 1/2, 25% is 1/4, 20% is 1/5, 12.5% is 1/8, 16.67% is 1/6, 33.33% is 1/3, 37.5% is 3/8 and 66.67% is 2/3. Calculating 12.5% of 480 becomes 480 divided by 8, which is 60, without any percentage arithmetic.
2. Use multipliers for successive changes
A rise of 20% multiplies a value by 1.2, and a fall of 20% multiplies it by 0.8. A 20% rise followed by a 20% fall is 1.2 multiplied by 0.8, which is 0.96, so the net change is a fall of 4%. The same idea handles successive discounts and compound growth: multiply the factors instead of adding the percentages.
3. Take a convenient base
When a question gives only ratios or percentages, choose a base that makes the numbers easy. For profit and loss, take the cost price as 100. For work problems, take the total work as the LCM of the days given. For a mixture problem, take the total quantity as a number that divides by the ratio parts.
4. Use ratios for time, speed and work
- When two objects travel the same distance, speed and time are inversely proportional. If A is twice as fast as B, A takes half the time.
- For equal distances at two speeds a and b, the average speed is 2ab divided by (a + b).
- If A is k times as efficient as B, A finishes in 1/k of B's time. Together they take the product divided by the sum of their times.
5. Use alligation for mixtures
When you mix two items of different value to get a mean value, the quantities are in the inverse ratio of the differences from the mean. If rice at 40 and rice at 60 are mixed to make 48, the cheaper to dearer ratio is (60 minus 48) to (48 minus 40), which is 12 to 8, or 3 to 2. This replaces an equation with one line of subtraction.
6. Estimate and eliminate
In a multiple choice question, you often do not need an exact answer. If the options are 16%, 19%, 21% and 25%, a quick estimate that gives about 20% already removes two options. Use estimation to narrow the choices, then calculate exactly only if two options remain close.
7. Check with digit sums and units
- Use the digit sum (mod 9) to check the result of an addition, subtraction or multiplication. If 47 multiplied by 36 is claimed to be 1,682, the digit sums are 2 times 0, which is 0, but 1 + 6 + 8 + 2 is 17 and the digit sum is 8, so the answer is wrong.
- Check the units at the end. A speed in km/h and a time in minutes must be converted before they are combined.
- Check that the answer is reasonable: a percentage above 100 or a negative length is a warning.
8. Know the squares, cubes and key values
Learn squares up to 30, cubes up to 15, and reciprocals such as 1/7 = 0.142857. These appear everywhere, in number system, geometry and estimation questions, and recalling them saves seconds that add up across a section.
How to practise
- Pick one shortcut a day and write it on a card.
- Solve ten questions using only that shortcut.
- Compare your time with the long method, and note the saving.
- Add the shortcut to your revision list only when you can use it without thinking.
- Test the whole set in a timed sectional test at the end of the week.
The CAT formula sheet lists the formulas behind these methods, and the guide to Quant study order shows which topics to learn first. Practise in timed conditions with our Quant practice tests.
Frequently asked questions
Are shortcuts enough to score well in CAT Quant?
No. Shortcuts speed up questions you already understand. You still need the concepts, so learn the reason first and the shortcut second.
Should I memorise tables and squares?
Yes, up to a sensible point. Squares to 30 and cubes to 15 are usually enough and save time in many questions.
How do I know when to skip a question?
If you have not found a way in after about 20 to 30 seconds, mark it and move on. You can return to it on the second pass.
Do shortcuts work for type in the answer questions?
Yes, and they are especially useful there, because you cannot use the options to check your result.