Mathematics and Stastics

Variance

Variance Variance (σ2) in statistics is a measurement of the spread between numbers in a data set. That is, it measures how far each number in the set is from the mean and therefore from every other number in the set. In investing, the variance of the returns among assets in a portfolio is analyzed as a means of achieving the best asset allocation. The variance equation, in financial terms, is a formula for comparing the performance of the elements of a portfolio against each other and against the mean. Variance is calculated by taking the differences between each number ... Read more

Time & Work

 TIME AND WORK In these problems the number of persons, quantity of work done and time taken are important factors. Also time taken by a person depends on the efficiency of that person which comes into picture when different people do the work such as women, children do the work alongside the men. The problems related to time and work can be solved by two major approaches – ratio & proportions and unitary method. Let us proceed to find some formulae related to these questions. Important Formulas – Time and Work If ... Read more

Time & Distance

 TIME & DISTANCE In this module we will deal with basic concepts of time and distance, speed, average speed, conversion from km/h to m/s and vice versa. This chapter will form the basis of further concept of relative speed which is used in train and boat problems. Important Formulas Speed=Distance/Time Distance=Speed × Time Time=Distance/Speed To convert Kilometers per Hour(km/hr) to Meters per Second(m/s)x km/hr=(x×5)/18m/s To convert Meters per Second(m/s) to Kilometers per Hour(km/hr)x m/s=(x×18)/5 km/hr If a car covers a certain distance at x kmph and an equal distance at y kmph, the average speed ... Read more

Surds And Indices

     Surds A surd is a square root which cannot be reduced to a rational number. For example,  is not a surd. However  is a surd. If you use a calculator, you will see that  and we will need to round the answer correct to a few decimal places. This makes it less accurate. If it is left as , then the answer has not been rounded, which keeps it exact. Here are some general rules when simplifying expressions involving surds.       am x an = am + n   am = am – n an     (am)n = amn   (ab)n = anbn     a n = an b ... Read more

Square Roots And Cube Roots

 Square Root & Cube Root   Step 1: First of all group the number in pairs of 2 starting from the right.   Step 2: To get the ten’s place digit, Find the nearest square (equivalent or greater than or less than) to the first grouped pair from left and put the square root of the square.   Step 3: To get the unit’s place digit of the square root   Remember the following If number ends in Unit’s place digit of the square root 1 1 or 9(10-1) 4 2 or 8(10-2) 9 3 or 7(10-3) 6 4or 6(10-4) 5 5 ... Read more

Simplification

 Simplification Simplification is one of the most important part of Quantitative Aptitude section of any competitive exam. Today I am sharing all the techniques to solve Simplification questions quickly. Rules of Simplification V → Vinculum B → Remove Brackets – in the order ( ) , { }, [ ]  O → Of D → Division M → Multiplication A → Addition S → Subtraction    Classification  Types Description Natural Numbers: all counting numbers ( 1,2,3,4,5….∞) Whole Numbers: natural number + zero( 0,1,2,3,4,5…∞) Integers: All whole numbers including Negative number + Positive number(∞……-4,-3,-2,-1,0,1,2,3,4,5….∞) Even & Odd Numbers : All whole number divisible by 2 is Even ... Read more

Simple Interest

 MATHEMATICS AND QUATITUATIVE APTITUDE – SIMPLE INTEREST Introduction Money is not free and it costs to borrow the money. Normally, the borrower has to pay an extra amount in addition to the amount he had borrowed. i.e, to repay the loan, the borrower has to pay the sum borrowed and the interest. Lender and Borrower The person giving the money is called the lender and the person taking the money is the borrower. Principal (sum) Principal (or the sum) is the money borrowed or lent out for a certain period. It is denoted by P. Interest Interest is ... Read more

Puzzle Test

 Puzzle Test Puzzle Test section comprises problems put in the form of puzzles involving certain number of items, be it persons or things. The candidate is required to analyse the given information, condense it in a suitable form and answer the questions asked.     In this type of test, the questions are based upon the given data belonging to different groups or possessing different qualities. These problems can be easily solved by constructing a proper table or chart.Read the question thoroughly .After reading the question, you will get the general idea on the question which has been ... Read more

Prepositions

 Prepositions Prepositions are short words (on, in, to) that usually stand in front of nouns (sometimes also in front of gerund verbs). Even advanced learners of English find prepositions difficult, as a 1:1 translation is usually not possible. One preposition in your native language might have several translations depending on the situation. The following table contains rules for some of the most frequently used prepositions in Prepositions – Time English Usage Example on days of the week on Monday in months / seasons time of day year after a certain period of time (when?) in August / ... Read more

Pipe And Cistern

 Pipes and Cistern   Inlet: A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as an inlet.   Outlet: A pipe connected with a tank or cistern or reservoir, emptying it, is known as an outlet.   If a pipe can fill a tank in x hours, then: part filled in 1 hour = 1 . x If a pipe can empty a tank in y hours, then: part emptied in 1 hour = 1 . y If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours ... Read more