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Shortcut for adding all even numbers or odd numbers

odd-numbers-even-numbersIn this article we will learn some shortcuts to add, if a series of odd number or even numbers are provided. For example in an examination it is asked, add all the ever numbers between 1 to 50 and then add all the odd numbers between 1 to 100 and then add both the results to get an answer. The trick to solve such kind of problems is  » » Continue to read » » »

Tricks for adding sequence of numbers

In this article we will discuss some nice time saving tricks for adding sequence of numbers.

A sequence of numbers can be represented as say 44, 45, 46, 47, 48, 49, 50, 51, 52. In this sequence we have smallest number as 44 and largest number as 52. There are in 9 numbers in this sequence. There are other type of sequence number as well. 4, 6, 8, 10, 12, 14, 16, 18, 20, 22 in this sequence we have smallest number as 4 and biggest number as 22. Similarly there can be other sequence as well like 7, 14, 21,, 28, 35 etc, here the numbers are increasing by 7 each time. or we can have sequence such as 3, 9, 27, 81, 243 where the numbers is 3 time of preceding number.

The numbers step up in sequence of 2’s. If we need to add all these numbers it can be a quite a task.

There is a very simple trick to do all this calculations » » Continue to read » » »

How to solve problems on ratio, proportion and variation

ratio proportions variationsRatio of the two terms is denoted by a:b and is measured by a/b. The a in the numerator is called as antecedent and the denominator b is called as consequent.

The ratio basically means how many multiples or parts is a of b. 

Proportion:  The numbers are in proportion when two ratios of the two terms are equal to ratio of other two terms, if a:b=c:d then a,b,c and d are in proportions

Variations:  The 2 quantities are said to be in direct or inverse proportion (variation) when a change in one quantity directly effects the other one. There can be direct effect that is known as direct proportion ( Like increase in “a” causes increase in “b”) and Inverse proportion when ( increase in “a” causes decrease in b).  » » Continue to read » » »

How to solve speed acceleration, marginal cost and rate of change type problems

The problems of the acceleration of speed or velocity, marginal cost, rate of change etc are often asked in competitive examinations. If you will notice all these type of problems common factor is incremental change, i.e. a variable is established, so here we not discussing about constant speed or constant cost etc.

All such type of problems are solved using the concept of function. We can explain by an example of acceleration,

We know acceleration is rate of change of speed, while speed is usually used with concept of fixed time and distance, velocity is often used with concept of distance covered over a period time in a specific direction.  » » Continue to read » » »

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