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Ratios and proportions

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Ratios and proportions is one of the most important topic in aptitude because of wide range of it's applications like ages, percentages, mixtures and allegations...
Ratio is a quantitative relation between two or more numbers which tells how many times one number is w.r.t other.

If a certain amount N is divided among A, B in a ratio a:b then
A's share is a/(a+b) * N and B's share is b/(a+b) *N
If A:B = a:b and B:C = c:d then A:C = a*c : b*d
If A:B = p:q, B:C = r:s, C:D = t:u then
A:D = A/D = (A/B) * (B/C) * (C/D)  
If a quantity is increased by a/b then the new content becomes (a+b)/b
If a quantity is decreased by a/b then the new content becomes (b-a)/b

To reduce your computations, it is always recommended to remember these values in terms of percentages
1/1 = 100 %
1/2 = 50 %
1/3 = 33.33 %
1/4 = 25 %
1/5 = 20 % 1/6 = 16.66 %
1/7 = 14.28 %       1/13 = 7.6%
1/8 = 12.25 %       1/12 = 8.33%
1/9 = 11.11 %       1/11 = 9.09%
1/10 = 10 %
Proportion is a number considered in …

prime numbers

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Prime numbers in Mathematics have a great property that they are divisible ONLY by '1' and by itself.

Traditional method to check whether a given number is prime number or not:
Check for the divisibility test for each and every number from 1-number but that is the worst strategy to solve problems based on prime numbers in aptitude.

Moderate method suggested to check for the Divisibility test for each and every prime or odd number from 1 to √(number) and this reduced some complexity in solving these problems.
Even this method failed to minimize the computation and thus a great concept of Prime Series came into existence which generalized the form of a prime number.

Generalized form of Prime number:  6*K ± 1 (K is a natural number)
"Every prime number is in the form of 6*K ± 1 " but not every  6*K ± 1 is Prime number.
To prove the above statement,
We can define each and every integer as (6*k-3) :Divisible by 3
(6*k-2) :Divisible by 2
(6*k-1)
(6*k+0) :Divisible by 6
(6…

Logarithm quantative aptitude question and answers

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Logarithms have a wide range of applications in solving problems which are based not only on logarithms but also on the problems like finding the bigger number of 2^51 and 5^30. Logarithms also have many other applications which when used gives an immense sense of its usage.
What is a Logarithm?
A Logarithm is a quantity which represents the rise of it in terms of another number (base)
How it was derived, is there any formula to get logarithmic values?
Yes, there is a series called logarithmic series which will generate value of the logarithms

The main terms which one should be more familiar with before solving logarithmic problems are
Exponent: Power of a number.
Base: The number to reduce another number when log is applied.
Some Basic Logarithmic formula:
log ab = log a + log b
log a/b = log a - log b
log(a^b) = b*log(a)
logab = 1/logba
logbn = logen/logeb
log10n = logen/loge10 = logen *(0.43429448..)

Tool to find logarithm value of a number
Calculate

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Playing with factorials

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Have you ever gone through factorial dependent questions in aptitude? Many problems which deal with factorials seems to be too complex and most of us may skip those questions even before a single try.so how can we stop these problems irritating or confusing us? well a few simple procedures to solve all such problems are given here
Before starting the procedures, let us learn about basics... Factorial(!): Product of an integer with all the integers below it. e.g: 4! = 4*3*2*1 The Highest power of a prime number 'P' (P is prime) in factorial of another number 'N' is
N/P + N /P^2 + N/P^3 + .....

Problems on trains aptitude tricks

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Voila, you are here!
Problems on trains in aptitude problems are not just to test your ability to solve the problems on trains and their properties but you can logically resolve many theories using this concept and this is one of the important part while learning aptitude.
Conversions:

A Kilometer/Hour = A(5//18) meter/second.A meter/second = A(18/5) Kilometer/Hour. Foundation: Time taken by a train of length 'l' units to cross a fixed point or pole is equal to the time taken by the train to travel 'l' units.Time taken by a train of length 'l' units to cross a  stationery object of length 'm' units units is equal to the time taken by the train to travel 'l+m' units.Suppose 2 trains are moving in the same direction with speeds U , V where U > V then their relative speed is U - V .

mixtures and alligations problems

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Alligation rule is used to determine the exact proportion to mix two ingredients of any price to obtain a mixture with estimated cost.

Mean price: Cost price of the mixture per unit.
suppose a container contains x units of liquid out of which y units are replaced then quantity of liquid after n such operations left in container would be x(1-y/x)^n 

Alligation rule: Quantity of cheap ingredient(b) : Quantity of costly ingredient (a)= x2-x1 : x1-x0
point to remember:
cost price of mixture always lies between two costs.
Consider the graph Quantity v/s Cost , with this method one can solve problems with more ease A: Type of cheaper ingredient. B: Type of costly ingredient.
x0: cost of cheaper ingredient.
x1: cost of mixture.
x2: cost of costly ingredient.
Quantity of cheap ingredient : Quantity of costly ingredient = x2-x1 : x1-x0


Deductions

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This is a part of Logical ability section, we are supposed to draw conclusions using given existing data but not from our usual life it's something life nature v/s nurture where we have to consider nurture but not generic nature, you will understand this by the end.
Example
All girls are women.
Some women are pregnants.
the conclusion can be: some girls are pregnants.(-or- some girls are not pregnants)

Deduction:
A form of reasoning with 2 premises and 3 terms.

Truth teller and lie detector problems

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The key idea of the truth teller identification in competitive exams is to test one's logical ability to answer questions and its usage is increasing day by day, It is the way to test your ability to identify the level truth or lie from many given inferences to draw some conclusion.From the given set of statements by few persons, has to draw a conclusion.


Truth teller,Lie Detector.   

Types of people in Truth teller and lie detector problems:





Liar : A person who always lie.Truth Teller :A person who always says the truth.Alternator: A person whose answers always alters in a step fashion(example: if he say 3 statements, his statements' truthness can be either T, F, T or F, T, F)

Simple Interest aptitude tricks

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Well we are all aware of calculating simple interest in our regular life and perhaps many solve this on the go,even though this post is for some one who is trying to figure out how to calculate simple interest for a loan lend or borrowed.

Terms:

Simple Interest(SI):Cash to be paid for using other's money. Principal(P): Amount lend or Amount borrowed.

Remainders in math expressions

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A Remainder is the portion is left unused after doing some process,In this context remainder is a number which is left when a number is divided by another number.

In the basic levels of our education,we learn how to find remainders of normal maths expressions like Remainder("5",4)=1 but what if the question is asked in the form of Remainder( "19*19*17*21*9" ,"5") calculation part requires more time than the time we get to solve the same in the exam if we follow traditional methods.
Divisor A number by which another number to be divided.