*Photo Credit: thethreesisters*

When you are competing against thousands or rather lakhs of people for a few seats, every minute matters. These days, probably what you did in your class 10^{th}, 12^{th} and graduation matters more than most things – but hey, you cannot do anything about that until someone invents a time machine. Although it can be debated whether it is fair / unfair / valid, etc. but I would like to reiterate – you cannot do anything about that. So, let us concentrate on something that you can do. You can work hard. You can do well in CAT and other exams. Here are a few tips and tricks which you can use to calculate faster in an exam.

__Calculating Squares__

**Type 1: Numbers ending in 5**

*If we remove the last digit ‘5’ from our number and are left with x, then the square will be [Product of x and x+1]25.*

**115^2**

First part = 11 * 12 = 132

Last part = 25

Answer = 13225

**395^2**

First part = 39 * 40 = 1560

Last part = 25

Answer = 156025

**Type 2: Numbers close to 50 **[41,59]

*Let the distance of the number from 50 be ‘d’. Then the square will be [25+d][d^2].*

**53^2**

Distance from 50 = 3

First part = 25 + 3 = 28

Last part = 3^2 = 9 = 09

Answer = 2809

**44^2**

Distance from 50 = – 6

First part = 25 – 6 = 19

Last part = (-6)^2 = 36 = 36

Answer = 1936

**Type 3: Numbers close to 100 **[91,109]

*Let the distance of the number ‘n’ from 100 be ‘d’. Then the square will be [n+d][d^2].*

**107^2**

Distance from 100 = 7

First part = 107 + 7 = 114

Last part = 7^2 = 49

Answer = 11449

**98^2**

Distance from 100 = – 2

First part = 98 – 2 = 96

Last part = (-2)^2 = 4 = 04

Answer = 9604

**Type 4: Numbers ending in 1,4,6,9**

*Calculate the square of the nearest multiple of 5. Add or subtract (Num + Multiple of 5) from it. If the multiple of 5 is bigger than the given number, then you subtract - otherwise add.*

**71^2**

Nearest multiple of 5 = 70

Square of the nearest multiple of 5 = 70^2 = 4900

Number + Multiple of 5 = 70 + 71 = 141

Answer = 4900 + 141 = 5041

**134^2**

Nearest multiple of 5 = 135

Square of nearest multiple of 5 = 135^2 = [13*14][25] = 18225

Number + Multiple of 5 = 134 + 135 = 269

Answer = 18225 – 269 = 17956

Now some of you might be thinking, “Where am I going to use this? This will come in handy in very few situations.” Well, I agree with you. Prima facie, it does look like something which might not come in handy on the first day or even the first week. But if you spend 10 minutes practicing the above tips, I can guarantee that you will save lot more time during your preparation. And if you can save some time during the exam, well that is a big fat bonus.

Having said that, given below is something that you can start using from today.

__Multiplying Two Digit Numbers__

In your normal way of multiplication, when you multiply 32 with 41, this is what you normally do:

For calculating faster, this is what you should do:

*Please – no jokes about my handwriting or the color combination.*

The idea here is instead of two steps, you should calculate the answer in just one step. Consider your answer as a combination of three parts

Last digit = Product of the last digits (may generate a carry, does not in this case) = 2 * 1 = 2

Second last digit = Cross product of the digits (may generate a carry, does in this case) = 3 * 1 + 2 * 4 = 3 + 8 = 11 = 1 written down and 1 carry

First part = Product of first digits (might include previous carry, does include in this case) = 4 * 3 + 1 = 1 3

Answer = 1312

Here are couple more examples to illustrate the idea further.

and

Hopefully, you will save some time using these tips, if not in the exam then at least in your preparation.

**Ravi Handa** has taught Quantitative Aptitude at IMS for 6 years. An alumnus of IIT Kharagpur where he studied a dual-degree in computer science, he currently runs www.handakafunda.com

2of3http://www.curiousmath.com/index.php?name=News&file;=article&sid;=52

But what I have noticed the the CAT attempt that I have taken, almost all of them can be solved with approximation and if I go to solve by vedic math, i will definitely be slower. The same I have seen with my students.

My take on CAT is that CAT does not check u on how fast you can calculate .. we have calculators to do that. But it tries to see how fast you can crack a problem with the best approach. So you will not find sums which are calculation intensive in cat. As a matter of fact if you understand the logic of the sums then getting an answer is just a formality.

1. 145/182=

Step1- add 10% to numerator and denominator

159/200=79.5 %

OA is 79.6 %

2. 532/745

adding 1% to numerator and denominator

537/750(approx)

adding 1/3rd

(537+179)/1000

716/1000=71.6%

OA-71.5

Please comment Giving more examples

Happy to solve them using the above Method

G.K

I know plethora of aspirants who do not know what is vedic maths

However, I agree partially with Patrick Sir, in that Vedic Maths is not necessary for best results; rather I feel it is preferable to develop one's own techniques and tricks - one simply has more confidence in something one has worked out from scratch. If you can do that, nothing like it. If not, well, Vedic Maths is the "poor man's option"!

@scrabbler I know you can learn some part of vedic math and it does help. Issue is there are different ways of cracking the exam. Vedic Math is for people like you who can understand Math to the core. Give an 2x2 calculation you can apply it to 3x3 or even a 4x4 sum. You are God in Math and in Math and I have no doubt you can apply anything anywhere.

But think of poor people like me who are not as good at Math. I do not know most of the theorem used in the pagalguy forums. People talk of Chinese Theorem and some other formulaes which I have no clue of. So if you give me a 2x2 multiplication I would not even bother to look at how to use it to 3x3 calculation . maybe sheer laziness. And I believe most of the students out there are like me who dont bother to understand the formula which they solve. Most of them just mug up the formula and use it in the exam. For poor souls like me, it is better to do the traditional methods. Suddenly if a 3x3 calculations come in the exam, I can use a uniform method of approximation instead of cluttering my mind with one more way of calculation or a formula .. my short memory does not permit me to remember too many things.

So what do I do. I follow what @scrabbler mentioned. Just try my own way. Shun formula. Understand the sum and solve it. Anyway most of the sums in the cat exam can be solved without using formula. And it works. This also works for most of the students who are non IITs .. a most of my students who get into IIMs are not even engineers. With such a poor grasp in Math, I have never scored less than 99.9%ile in Math or DI section (except one year) in the last 7 years I have taken CAT and even managed to score a few 100%ile in the section.

I apply the same thing for calculations. Instead of cluttering my mind with various rules for vedic math, I have found approximations comfortable ... again could be sheer laziness to remember the rules.

3of355*55

Multiply the last digit of the two numbers i.e. 5*5 =25. Here, 5 becomes the last digit of the result and 2 is carried forward.

Add the 1st digits of the two numbers i.e. 5+5 = 10. Multiply it with the last digit of the number i.e. 10*5 = 50 +2 ( carried forward) i.e. 52. 2 becomes the second last digit of the result and 5 is carried forward.

Multiply the 1st digits of the two numbers i.e. 5*5 = 25 + 5 (carried forward) i.e. 30 needs to be added as the prefix to the result.

So, 55*55 = 3025

need some practice will more effective ...