Quantitative Aptitude


Tables are very commonly used to represent the set of related data. Tabulation is a very popular technique of data interpretation in which a set of questions are derived from a given table of data or observations.

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Line Charts

A line chart or line graph is a kind of chart to display information as a series of data points called 'markers'. These markers are connected by straight line segments. It is a very commonly used chart in many fields. Normally measurement points are ordered by their x-axis values and joined with straight line segments. A line chart is normally used to visualize a data trend over the periods of time or to represent a time series drawn chronologically.

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Pie Charts

A pie chart (or a pie graph) is a circular statistical graphical chart, which is divided into slices in order to explain or illustrate numerical proportions. In a pie chart, central angle, area and an arc length of each slice is proportional to the quantity or percentages it represents. Total percentages should be 100 and total of the arc measures should be 360°. Following illustration of pie graph depicts the cost of construction of a house.

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Bar Charts

A bar chart or bar graph is a type of chart to represents Grouped data with rectangular bars where lengths of rectangles or bars are proportional to the values that they represent. The bars can be plotted or drawn vertically or horizontally. A vertical bar chart is also called a column bar chart.

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Chain Rules

Rule of three

The method of finding the 4th proportional when the other three are given is called Simple Proportional or Rule of three.

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Solving problems on ages is a two step process.

  1. Create linear equations based on statements provided.

  2. Solve the equations to get the values as required ages.

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Stock Market

To begin a major business or an industry a lot of cash is required. It is past the limit of maybe a couple persons to orchestrate such an immense sum. Be that as it may, a few persons relate together to form an organization They then draft a proposition issue an outline (for the sake of the organization), clarifying the arrangement of the undertaking and welcome people in general to put cash in this venture, They, pool up the assets from the general population, by relegating then shares of the organization.

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While simplifying an expression, the VBODMAS must be learnt as V,B,O,D,M,A,S where every alphabet have a special stand which are as follows:

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Races & Games of Skill


A contest of speed in running, riding, driving, sailing, rowing is called a race.

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A succession of numbers formed and arranged in a definite order according to a certain definite rule is called a sequence.

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Pipes & Cisterns

  1. Inlet: A pipe connected with a tank or cistern or a reservoir, that fills it, is known as an inlet.

  2. Outlet: A pipe connected with a tank or cistern or reservoir, emptying it is known as an outlet.

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Speed and Distance


Speed = DistanceTime
Time = DistanceSpeed
P km/hr = (P x 518)m/sec
P m/sec = (P x 185)km/hr

If the ratio of the speeds of P and Q is p:q, then the ratio of the times taken by them to cover the same distance is

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Basic Equations

Linear equations in two variables

An equations of the form ax + by +c= 0, where a, b, c ⊂R and a≠0 , b≠0 and x ,y are variables, is called a linear equation in two variables.

Solution: Any pair of values of x and y which satisfy the equation ax + by + c =0, is called its solution.

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A point is an exact location

Line Segment

The straight path between two points A and B is called a line segment AB. A line segment has two end points.

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Co-ordinate Geometry

Position of a point in a plane

In coordinate geometry, points are placed on the "coordinate plane" as shown below. It has two scales - one running across the plane called the "x axis" and another right angle to it called the y axis. (These can be thought of as similar to the column and row in the paragraph above.) The point where the axes cross is called the origin and is where both x and y are zero.

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Important Terms

  1. Speed in km/hr

    a km /hr = (a * 5 / 18) m/s.
  2. Speed in m/s

    a m/s = (a * 18/5) km/hr.

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Boats & Streams

  1. In water, the direction along the stream is called Downstream. And the direction against the stream is called Upstream.

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Time & Work

  1. If A can do a piece of work in n days, then A's 1 day work = 1/n.

  2. If A's 1 day work = 1/n, then A can finish the work in n days.

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When some money is invested by two or more people jointly then they are called partners and under an agreement they invested money is called partnership.

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Simple Interest

  1. Simple Interest: If the interest on a sum of money borrowed for a certain time period is reckoned uniformly, it is called as Simple Interest.

  2. If Principal = P, Rate = R% per annum, Time = T years, then

       Simple Interest (S.I) = P * T * R / 100

    The above expression involves four quantities: P, I, T and R. If three of them are known to us,the fourth one can be easily found out.

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The face or dial of a watch is a circle whose outline is partitioned into 60 equivalent amounts of, called moment spaces.

A timekeeper has two hands, the littler one is known as the hour hand or short hand while the bigger one is known as the moment hand or long hand.

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Odd days: In a given period, the quantity of days more than the complete weeks are called Odd days.

Leap Year: Every year divisible by 4 in a leap year. But not all century years are leap years. Only those century years which are divisible by 400 are leap years and other century years are ordinary years. As an example, 1100, 1300, 1400, 1500, 1700 are ordinary years but 1200, 1600, 2000 are leap years. So every 4th century is a leap year.

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Important Fact and Formulae

Following are important facts and formulaes used in questions for volume calculations.

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Important Fact and Formulae

Following are important facts and formulaes used in questions for area calculations.

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Squares & Cubes

Square Root

When y = x2 then square root of y is x and it is written as √y = x.

For example, √9 = 3, √16 = 4 and so on.

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Height & Distance

Angle of Elevation

The angle of elevation of an object as seen by an observer is the angle between the horizontal and the line from the object to the observer's eye (the line of sight).

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Profit & Loss

  1. Cost Price, (c.p.) = The price, at which an article is purchased, is called its cost price.

  2. Selling price (s.p) = The price, at which an article is sold, is called its selling price.

  3. Profit or Gain = (S.P) - (C.P)

  4. Loss = (C.P) - (S.P)

  5. Gain or Loss is always reckoned on C.P.

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Average = (Sum of ObservationsNumber of Observations)

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Suppose a man has to pay Rs. 156 after 4 years and the rate of interest is 14% per annum. Clearly, Rs. 100 at 14% will amount to R. 156 in 4 years. So, the payment of Rs. now will clear off the debt of Rs. 156 due 4 years hence. We say that:

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Factors and Multiples

If a number P divides another number Q exactly, we say that P is a factor of Q i.e. Q is a multiple of P.

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Ratio represents the proportion in which a number contains another number. A ratio is represented by a/b or a:b. The duplication or division of every term of a proportion by the same non zero number does not influence the proportion.Subsequently, 3:5 is the same as 6:10 or 9:15 or 12:20 and so on.

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Percent means many hundredths.Example: z% is z percent which means z hundredths. It will be written as:

z% = z100

pq as percent: (pq x 100)%

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Decimals & Fractions

Decimal Fractions

Fractions having denominators in power of 10 are called decimal fractions.

 1/10 = .1, 2/10 = .2, ....
 1/100 = .01, 2/100 = .02, ...
 1/1000 = .001, 2/1000 = .002, ...

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Basic Arithmetic


A sequence represents numbers formed in succession and arranged in a fixed order defined by a certain rule.

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Number System


In Decimal number system, there are ten symbols namely 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 called digits. A number is denoted by group of these digits called as numerals.

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