Bonus for the weekend!

I thought of adding another small trick which is pretty helpful as the week comes to an end.This has also been a pretty useful trick but has an underlying assumption.The trick is about calculating square on a number given the square of the preceding or the succeeding number.The funda comes from a formula which most of us would have done as a start to algebra in class 6th.The formula is and I think all of you would remember it-

a^2-b^2=(a-b)(a+b)

For the uninitiated ^ implies the 'raised to the power of ' sign.

Funda-To calculate the square on a number without multiplying it by itself you can use the following technique if you have the square of the preceding number with you.

1)Add the 2 consecutive numbers

2)Add the sum to the square of the preceding number.

3)In this case the (a-b) term becomes 1 and that is what makes the difference of the squares the sum of the numbers.

Let me elucidate with an example.

Example-Let me calculate the square of 76 for you guys.I hope everyone knows the square of 75.If you dont you can learn this trick about calculating squares of numbers ending with 5(Believe me this is justs the tip of the iceberg).The square will always end with the last two digits as 25.The first few digits can be calculated by multiplying the number preceding 5(in this case 7) with the next number(in this case 7+1=8).The multiplication of 7 and 8 will give us 56 which become the first 2 digits of the square giving us the answer as 5625.

Now that we have the square of 75 we follow the steps mentioned

1)Add 75 and 76 to get 151

2)Add 151 to the square of 75 i.e. 5625

3)The sum i.e. 5776 is your answer

The underlying assumption that I mentioned before is that you should be quick enough with your additions and should know the squares of some important numbers atleast.

Hopefully you enjoyed this funda and can come back next week when I really start with some amazing revelations.Until then Happy Solving!

A gentle start..

Let me talk about two pretty basic things today.These things may not have a lot of direct applications but you will find them useful if you begin using them regularly.In my experience,they have helped me a lot in doing my calculations faster and hopefully they will help you guys too.Here it goes-

a)The average of two numbers-

This trick will help you calculate the average of two numbers in a different way from just adding them and dividing them by 2.I will show you the application after I highlight the funda.Lets say we have two numbers a and b.We can find their average by-

1-Subtract the smaller number from the larger one

2-Divide the difference by 2.

3-We get the average by either adding the answer obtained in 2 to the smaller number or subtracting the same from the larger number.

For example-I have two numbers 4 and 8.I subtract 4 from 8 to get 4.I divide 4 by 2 to get 2.And I add 2 to 4 or subtract 2 from 8 to get the average as 6.

Application-Now this seems pretty weird right?I mean its basically increase of a step from the general method.But the application comes in when you look to calculate the average of 2 numbers which are easier to subtract than add.

Case in point-999 and 1999.The difference is 1000.I get 500 when I divide it by 2.And when I add it to 999 or subtract it from 1999 I get the average which is 1499.

Believe me once you start using this frequently you will become so comfortable with it that you will use it subconsciously.

Note-This can only be used to find the average of 2 numbers.

b)Digital Sum

First of all let me explain what digital sum is.It is as the name specifies the sum of all the digits of a number until you have just a single number.

For example-The digital sum of 887 is 5(8+8+7=23;2+3=5)

Now that you know what digital sum is the point I want to make is-

Funda-The sum of the digital sum of 2 numbers is the digital sum of the sum of the same 2 numbers.

Confused?Read it again and understand it.

Example-What is the sum of the digital sums of 23 and 45?

Now either you can calculate the digital sums of 23 and 45 separately(5 and 9 respectively) and add the two.This gives the answer as 5(5+9=14;1+4=5)

Or you could add the two numbers which will give you 68.The digital sum of 68 is also 5(6+8=14;1+4=5)

Additional note-For any number with any number of 9s and a few other digits,the digital sum can be calculated by ignoring the 9s.

That is to calculate the digital sum of 9698 I just need to add 6 and 8 to get the digital sum as 5.You can add all the 4 numbers and you will get the same answer.Try it..9+6+9+8=32 which also gives the digital sum as 5.

That is all for today.I will be coming out with more advanced concepts in further posts.Hope you all enjoyed reading the 2 fundae for today and that you come back for more.

A New Initiative!

I have had this idea in my head for a few days now to start a blog related to numbers.During my 1.5 years of teaching and getting taught for CAT,I think I have developed quite a few tips and tricks which should be very helpful to people as far as various MBA entrance exams are concerned.

Apart from my CAT prep I have always had a interest in numbers and have looked to develop my own ways of quickening calculations.

So here it goes.Watch out for some tricks that are sure to blow your mind..

Happy Reading..