Short Tricks of Maths for Exams

Speed matters in SSC, banking, railway and campus-placement aptitude papers. Most students lose time not on hard questions but on ordinary arithmetic: multiplying two-digit numbers, finding squares, working out percentages. A few short tricks remove that bottleneck.

Below are nine tricks that come up again and again in competitive exams. Each one is shown with a worked example so you can check it yourself.

1. Multiply any two-digit number by 11

Write the two digits apart and put their sum in the middle.

• 52 × 11: 5 and 2, middle = 5 + 2 = 7, answer 572
• 87 × 11: 8 and 7, middle = 15, carry the 1 to the left: 957

2. Square any number ending in 5

Multiply the first part by the next number, then write 25 at the end.

• 65²: 6 × 7 = 42, then 25, answer 4225
• 115²: 11 × 12 = 132, then 25, answer 13225

3. Multiply numbers close to 100 (base method)

Find how far each number is below 100. Subtract one deficit from the other number, then multiply the deficits.

• 97 × 94: deficits 3 and 6. Left part = 97 − 6 = 91. Right part = 3 × 6 = 18. Answer 9118

4. Square numbers close to 50

For a number 50 + d, the left part is 25 + d and the right part is d², written as two digits.

• 47² (d = −3): 25 − 3 = 22, and 3² = 09, answer 2209
• 53² (d = 3): 25 + 3 = 28, and 09, answer 2809

5. Multiply by 5 in one step

Multiply by 10 and halve.

• 468 × 5 = 4680 ÷ 2 = 2340

6. Turn percentages into fractions

Memorise a short table and percentage questions become one division.

• 37.5% of 640 = 3/8 × 640 = 240

7. Successive percentage change

Two changes of a% and b% give a net change of a + b + ab/100.

• A price rises 20% and then falls 10%: 20 − 10 − (20 × 10)/100 = +8%

8. Check a multiplication with digit sums

Reduce each number to a single digit by adding its digits. The product of those digits, reduced the same way, must match the reduced answer.

• 237 × 46 = 10902? 237 gives 3 (2+3+7 = 12, 1+2 = 3), 46 gives 1 (4+6 = 10, 1+0 = 1). 3 × 1 = 3. The answer 10902 gives 1+0+9+0+2 = 12, 1+2 = 3. It matches.

This does not prove an answer right, but it catches most slips in seconds.

9. Divisibility by 11

Take the alternating sum of the digits from the left. If it is 0 or a multiple of 11, the number is divisible by 11.

• 918082: 9 − 1 + 8 − 0 + 8 − 2 = 22, a multiple of 11, so it divides exactly (918082 ÷ 11 = 83462)

How to practise

Learn two tricks a day, and do ten questions with each before moving on. After a week, mix them in a timed set of 30 questions. The aim is to stop thinking about the trick and simply see the answer.

Go further

These nine are a starting point. Our book Short Tricks of Math collects many more shortcut methods with worked examples, built for quick practice before exams. For broader preparation, browse the Exam Prep Series and our Basics of Math.