If you are a bit slow in Quantitative Aptitude problems in Mathematics, which generally appears in many competitive exams like CAT, AFCAT, SNAP, XAT, IIFT etc… These tricks will only be helpful if you at least remember Tables up to 20 and can do addition of two numbers very fast. If you are not at that level, then practice first, come back here latter.

Various techniques which I use in problem solving are-

- Digital Sum Technique
- Divide and Rule Technique
- Using Algebraic formulas
- Percentages
- Vedic Mathematics
- Russian Peasant Mathematics
- Base Method
- Duplex Method

And there is no end to this list as you get deep into mysteries of mathematics. I will be briefing about these methods in this post, with the links to original source articles for further explanation. If you got any doubts, please let me know through comments section.

- Digital Sum Technique-

As we work on decimal number system, it is inherent property of a number to retain its digital sum even when it is multiplied, divided, added or subtracted.

Digital sum is sum of digits with which a number is made, till we get a single digit number, for example

753729026 has digital sum = 7+5+3+7+2+9+0+2+6 = 41 = 4 + 1 = 5. Now if we do any operation with this number our basic mathematics operations can be easily verified with this technique, Example-

753729026 X 2132 = 1609650283432

Writing digital sum of each number-

753729026 => 5

2132 => 8

1609650283432 => 4

Multiplying digital sums – 8 X 5 = 40 (digital sum = 4)

So this method might help you in quick verification of calculation or answer option elimination.

- Divide and Rule Technique-

Suppose you have to perform a lot of calculation, you can arrive at an approximate answer using this technique-

Example- Find 13.8 X 6.3 + 173% of 600

Now, divide and rule by breaking them into parts

This can be written as-

13 X 6 + 0.8 X 6.3 + 0.3 X 13.8 + 175% of 600 – 2% of 600 = 72 + 5 + 4 + 7/4 of 600 – (2 x 1% of 600)

= 83+ 1050 – (2×6) = 1121 (approximately)

1124.94 (Exactly)

Hence using this we got an error of 0.35% and calculation can be done mentally.

- Using algebraic formulas-

Keep some of the algebraic formulas in your mind like-

a^{2}– b^{2}= (a-b) (a+b)

Example – 22^{2}– 13^{2}= 9 x 35 = 315

There are lot more other formulas too, lookout for them.!

- Percentages

Well, if you know all the percentages and corresponding fractions, a lot of hard work can be reduced!

Try learning the common percentages, some of these are shown below-

- Vedic Mathematics

I use this to do faster multiplication. See example below-

Multiply and write the numbers as shown.

- Russian Multiplication

To use this you need to be very fast in doubling the numbers and arriving at halves as well. Here is a quick demo how to perform such multiplication.

- Base Method

This one is applicable to digits near same base, like here is an example-

- Duplex Method

This one is used in calculating squares as shown below-

References-

- http://mathworld.wolfram.com/RussianMultiplication.html
- http://en.wikipedia.org/wiki/Digital_root
- http://www.sciencenews.org/view/generic/id/8203/title/Math_Trek__Divide-and-Conquer_Multiplication
- http://en.wikibooks.org/wiki/Vedic_Mathematics/Techniques/Multiplication
- Bonus – Japanese Multiplication