# SEP23 – Problems on Numbers

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Today, We are going to take a test on Problems based on Problems on Numbers

Before you take the test read these posts to be comfortable.

Important Formulae

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.

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

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#### SEP23 - Problems on Numbers

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