M4apt

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.

One of the important roles of an organization is to ensure the overall performance based on profit as it is the only factor for organization's sustainability.so profit and loss problems have a great role in quantative aptitude. In general,profit can be defined as the financial gain and loss can be defined as the amount lost. There are few more terms which one should learn  Cost Price(C.P): Amount incurred for purchasing/manufacturing the product. Selling Price(S.P): Gained amount in process of selling the product.

Many exams try to make you feel that you cannot solve the problem by making question as big as possible like units place of (186937)^178909 but solving this problem is as simple as solving 9%4 Before solving these kind of problems, understand the great concept called Cyclicity of numbers which states that any digit when multiplied by itself repeatedly, generates a cycle of digits. points to remember: Only units place will be responsible for generating units place Every number after applying successive multiplications,repeats the cycle of digits. So try to figure out a common series in powers of digits for example units(3)=3,units(3*3)=9,units(9*3)=7,units(7*3)=1,units(1*3)=3(we get a cycle of multiplication) Number      powers                         Series/cycle(units place of powers column) [cyclicity of number] 2                 2,4,8,16,32                   2,4,8,6                    [4] 3                 3,9,27,81,243               3,9,7,1              

In the direction based problems, we should generally determine the direction or distance if a person travels in a path with many lefts or rights and turns in a certain direction. Basic things which we need to keep in our mind while solving direction based problems includes the direction compass. If we measure the angles between directions, the angle between two successive directions is 90 degrees.

In the pipes and cistern problems, the majority of the problems deals with Inflow,outflow,current capacity, full tank,empty tank. There will be few inlets connected to a dam or tank through which water enters into dam or tank and outlet through which water exits the tank or dam. cistern: A tank to store water. Important points. If pipe can fill the tank in 'x' hours then rate of flow is 1/x(1/x portion of tank gets filled in 1 hour)(when we divide the tank into x parts,one part gets filled in a unit of time) If pipe can empty the tank in 'y' hours then emptying rate is 1/y(1/y portion of tank gets emptied in 1 hour)

L.C.M can be defined as Least Common Multiple of all the numbers. H.C.F can be defined as Highest Common Factor of all the numbers. Important formulae: LCM*HCF=product of the numbers. If any number is factor of other then LCM is bigger one and HCF is the other. In general to find LCM,we need to write all the multiples of given numbers and find common number in the series similarly to find HCF of few given numbers,we need to find all factors of given numbers and identify big such factor common for both the numbers but this is a time taking process so we are here for you with some other trick. First let us know about the traditional methods to find LCM,HCF. In traditional method,to find LCM of 4,15 we have to write multiple series of both the numbers. Identify common number in both. Multiples of 4: 4,8,12,16,20,24,28,32,36,40,45,58,52,56, 60 ,64......... Multiples of 15: 15,30,45, 60 ,75.......... we can say 60 is LCM of 4,15 but this takes more time. I

Prime factorization is a method of representing a number in terms of multiples of prime numbers which is more powerful in identifying co-primes, LCM, HCF, number of its factors. What are prime numbers? These are the numbers which have no factors other than one and itself. Divide and rule was