Tricks for fast Addition of numbers

Here is another post on basic quantitative aptitude techniques, particularly concerning shortcut techniques in integer  addition Some of these are very easy to follow, still if you are not able to get something, please use the comments box to start the discussion on that particular topic.

Trick 1 : Adding Consecutive Numbers

Any set of consecutive numbers can be added by this simple relation-
Sum = (Last Number – First Number + 1) * (First Number + Last Number)/2

For example, you need to add numbers from 30 to 40, then…
Using the above relation, we get, Sum = (40-30+1) * (40+30)/2 = 11*70/2 = 385

Trick 2 : Sum of Odd numbers from 1 to n

This one is very easy. Sum of odd numbers from 1 to n is ((n+1)/2)2.
For example, 1+3+5+7+9+11+13+15+17+19+21 = ((21+1)/2)2 = 112

Trick 3 : Sum of Even numbers from 2 to n

To find this, use this relation-
Sum = (n/2)*((n/2)+1)
For example, to find sum up to 100, use this relation-
Sum = (100/2) * ((100/2)+1) = 50 * 51 = 2550

However these tricks are pretty obvious and very small, but when used in competitive exams like CAT and UPSC, these can be valuable resource in reducing the time required per question.

Check out a few more related posts here-

  1. Quantitative Aptitude Techniques
  2. Syllogism Cheat Sheet