PROBLEMS ON NUMBERS -> DESCRIPTION

In this section, questions involving a set of numbers are put in the form of a puzzle. You have to analyse the given conditions, assume the unknown the numbers and form equations accordingly, which on solving yield the unknown numbers.

AVERAGE -> IMPORTANT FACTS AND FORMULAE 

I. Average = [Sum of observations / Number of observations] 

II. Suppose a man covers a certain distance at x kmph and an equal distance at y kmph. Then, the average speed during the whole journey is [2xy / x + y] kmph.

Numbers -> IMPORTANT FACTS AND FORMULAE 

1. Natural Numbers : Counting numbers 1, 2, 3, 4, 5, .. are called natural numbers. 

II. Whole Numbers : All counting numbers together with zero form the set of whole numbers. 

Thus, I. 0 is the only whole number which is not a natural number.  

II. Every natural number is a whole number. 

III.Some Important Formulae :

 I. ( 1 + 2 + 3 + .....+ n) = n (n + 1 ) / 2 

II. (1 2 + 22 + 32 + ..... + n2) = n ( n + 1 ) (2n + 1) / 6 

III. (1 3 + 23 + 33 + ..... + n3) = n2 (n + 1)2 / 4