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Welcome ToJSpiders Aptitude

Quantitative General Reasoning Aptitude English

PREFACE

We are all set to start Quantitative Aptitude and so, first we must know:

What is Aptitude What is Aptitude Test and why IT companies have kept aptitude test as the first road block to be cleared to

proceed to the next round.

Aptitude is a natural ability to do something or to learn something or in other words it is inclination or capacity for learning. And Aptitude test is a standardized test designed to predict an individual’s ability of learning skills. How fast an individual can learn skills and how efficiently he can deliver it. And this is what makes it very important. Once you cleared the Aptitude test you will get required momentum to sail through next stages as well. It will provide enough confidence and right attitude and glory will be yours.

Well biggest roadblock in doing aptitude is lack of interest shown by students. And most of the time I have seen that instead of having all technical skills, students fail to deliver at aptitude. Let me tell you if you understand how to approach it will be one of your very strong points.

To make it easier I have made two parts to be focused on.

Preparation Part Personal Part 1. Calculation 1. Self- motivation and determination2. Relation or Relate the given quantity 2. Perseverance.3. Trick 3. Right guidance and4. Speed 4. Horripilation.5. Hitting the right question and

6. More and more tricks

Once I come to this point and explain it all, you will discover yourself how it works.

I will always endeavor to deliver my best and once I am completed, I will strive not to leave any place for skepticism. My effort will be to make it as interesting as possible.

Our student's constructive feed back and suggestions are most welcome and highly appreciated. I will be highly obliged if you message /email me your feedback or suggestion on shambnu060@gmail.com.

S Kumar

CONTENTS

1. Basics2. Number System3. H C F and L C M4. Simplification5. Square Roots and Cube Roots6. Average7. Problems on Numbers8. Problems on Ages9. Percentage10. Profits and Loss11. Ratio and Proportion12. Partnership13. Chain Rule14. Time and Work15. Pipes and Cistern16. Time and Distance17. Problems on Train18. Boats and Streams19. Allegation or Mixture20. Simple Interest and compound Interest21. Area, Surface Areas and Volumes 22. Clocks23. Permutations and Combinations24. Probability25. Heights and Distances (Trigonometry)26. Odd man out Series27. Geometry28. Data Interpretation29. Races30. Calendar31. Series32. Set Theory33. Linear Equations34. Quadratic Equation

IMPORTANT POINTS AND FORMULAS

1. Number SystemI. Divisibility Rules

II. Unit digit numbers

2. H.C.F and L.C .MI. Product of two numbers = HCF×LCM

3. Average

I. Average = ∑ of Observation

Totalnoof observations

II. If a man covers a certain distance at xkmph and an equal distance at y kmph

Then the average speed during the whole journey =2xyx+ y

kmph

4. Percentage

I. x % = x100II. If the price of commodity increases by R% then the reduction in consumption so as not to increase the

expenditure is= [ R100+R

×100]%III. If the price of a commodity decreases by R% then the increase in consumption so as not to decrease the

expenditure is= [ R100−R

×100 ]%IV. Let the population of a town be now be P and suppose it increases at the rate of R% per year then

Population after n years = P(1+ R100 )

n

Population n years ago ¿ P

P (1+ R100 )

n

V. Results on depreciation : Let the present value of a machine be P suppose it depreciates at the rate of R% per anum then:

Value of the machine after n years= ¿ P(1− R100 )

n

Value of the machine n years ago=

P

P (1− R100 )

n

VI. If A is R% more than B, then B is less than A by [ R100+R

×100]%VII. If A is R% less than B, then B is more than A by [ R

100−R×100 ]%

5. Profit and Loss

C.P = cost price S.P = Selling Price

I. Gain=S . P−C .P and Gain% = (Gainc . p×100)

II. Loss=C . P−S . P and Loss% =( Lossc . p×100)

III. S.P when

There is profit S .P=(100+Gain%)

100×C . P

There is loss S .P=(100−loss%)

100×C .P

Sequestered:- (of a place or person) isolated and hidden away, secluded, cloistered, cut off, secretTo seize property until a debt has been paid

IV. C.P when

There is profit C . P= 100(100+Gain%)

×S . P

There is loss C . P= 100(100−loss%)

×S .P

6. Ratio and Proportion

I. Ratio: - The Ratio of two quantities a and b in the same units is the fraction aband written as a: b.

II. Proportion :- The equality of two ratios is called proportion so a:b = c:dIII. Fourth proportional: - If a: b=b: c, then c is called the fourth proportional of a, b and c.IV. Third proportional: - If a: b= b: c, then c is called the third proportional.

V. Mean proportional:- Mean proportional between a and b is √abVI. Duplicate ratio of (a:b) is (a2, b2)

VII. Sub – Duplicate ratio of (a:b) is (√a ,√b)

7. Partnership

I. Ratio of division of Gains:i. When investment of all partners are for the same time. The gain or loss is distributed

among the partners in the ratio of their investments.ii. When investments are made for different time periods , then the equivalent capitals time

periods then the equivalent capitals are calculated for a the given investments. Suppose a invests X for P months and B invests Y for Q months , then (A'S share of profit) :( B’S share of profit) = XP: YQ

8. Time and Work

I. If A can do a piece of work in n days then A'S 1 day’s work = 1/nII. If A'S 1 days work = 1/n then A can finish the work in n days

III. If ratio of work done by A and B is 3:1

Then ratio of time taken by A and B to finish the work is 1: 3

9. Pipes and Cisterns

I. Inlet: - A pipe connected with a tank, a cistern or a reservoir that fills it is known as an inlet.II. Outlet:- A pipe connected with a tank, a cistern or a reservoir emptying it is known as an outlet.

III. If a pipe can fill a tank in x hours then part filled in 1 hour = 1/xIV. If a pipe can empty a full tank in y hours then

Part emptied in 1 hour = 1/y

V. If a pipe can fill a tank in x hours and and other pipe can empty the full tank in y hours (y>x) , then opening both the pipes the net part filled in 1 hour

= 1x− 1

y

VI. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (x>y) .Then opening both the pipes the net part emptied in 1 hour

= 1y−1x

Proponent:- a person who advocates a theory or proposal, advocate, protagonist, supporter, patron, apostle

10. Time and Distance

I. Speed = DistanceTime , time =

DistanceSpeed , Distance = (speed × time)

II. x km/hr = ( x×518) m/sec and x m/s = (x×

185 )km/hr

III. If the ratio of the speeds of A and B is a:b,then the ratio of the time taken by them to cover the

same distance is 1a: 1bor b:a

IV. Suppose a man covers a certain distance at x km/hr and an equal distance at y km/hr , then the

average speed during the whole journey is (2xyx+ y

)km/hr.

11. Problems in trains

I. If a train of length L meters is to pass a man, a pole or a signal post then distance travelled by train is L

meters.

II. If a train of length L meters is to pass a stationary object of B meters then distance covered by train is

(L+B) meters.

III. If two trains of speed u m/s and v m/s are moving in the same direction then their relative speed

= (u-v) m/s where (u>v)

IV. If two trains of speed u m/s and v m/s are moving in the opposite direction then their relative speed

= (u + v) m/s

V. If two trains of length a meters and b meters are moving in opposite directions at u m/s and v m/s, then

time taken by the trains to cross each other = ( a+bu+v )sec

VI. If two trains of length a meters and b meters are moving in the same direction at u m/s and v m/s (u>v)

then time taken by faster train to cross the slower train = ( a+bu−v )sec

VII. If two trains start at the same time from points A and B towards each other and after crossing they take a

and b sec in reaching B and A respectively then ( A'S speed) :(B'S speed) = (√b: √a)

12. Boats and Streams

I. Downstream:- the direction of boat along the stream is called downstream.II. Upstream:- The direction of boat against the stream is called upstream.

If the speed of a boat in still water is u km/hr and speed of the stream is v km/hr then

Speed downstream = (u + v)km/hr Speed upstream = (u-v) km/hr

III. If the speed downstream is a km/hr and speed upstream is b km/hr then

Speed of boat in still water = 12

(a + b)km/hr

Speed of stream = 12 (a-b)km/hr

Desultory :-lacking purpose or enthusiasm, lukewarm, haphazard, erratic ,unmethodical

13. Alligation or Mixture

C.p of a unit of cheaper item c.p of a unit of dearer item

Mean price

d - m m - c

so, (cheaper quantity):(dearer quantity )= (d-m ) : (m-c)

Suppose a container contains x units of liquid from which y units are taken out and replaced by water. After n operations, the quantity of pure liquid

=[ x(1− yx )¿¿n]¿units

14. SIMPLE INTEREST AND COMPOUND INTEREST

I. S.I=P×R×T100

II. Compound interest

Let Principal=P, Rate=R% and Time=n years

i. Amount=P= P(1+ R100 )

n

[when interest is annually]

And C.I= A-P

ii. A=P= P(1+ R2×100 )

2n

[when interest is half-yearly]

And C.I=A-P

III. When rates are different for different years, say R1%, R2% and R3% for 1st, 2nd and 3rd year respectively

Then amount= P(1+ R1100 )(1+ R2

100 )(1+ R3100 )

15. Area, Surface Area and Volume

I. Rectangle Area of Rectangle= Length × Breadth

So length=Area/Breadth and Breadth=Area/Length

Perimeter of Rectangle=2(L+B)II. Square

Area of square=( side )2=12 (diagonal )2

length of diagonal of a square=√2 × sideIII. Triangle

Area of a triangle=12 × Base × Height

Area of a Triangle=√s (s−a)(s−b)(s−c )

Truncate: - shorten by cutting off the top or the end , curtail, retrench

Where a, b, c are the side of the triangle and s=a+b+c2

Area of an equilateral triangle=√34

×side2

Radius of an in circle of an equilateral triangle of side a= a2√3

Radius of circum circle of an equilateral triangle of side a= a√3

IV. Quadrilateral Area of a parallelogram= Base× height

Area of a rhombus=12 (product of diagonals)

Area of a Trapezium=12 (sum of parallel sides × distance between them)

V. Circle

area of a circle¿ π r2

Perimeter of a circle=2π r

length of an arc of circle= θ360 ×2π r (where θ is the central angle)

Area of a sector== θ360 ×π r2

Area of a semi- circle=π r2

2 Circumference of a semi circle=π r Perimeter of a Semi- circle=π r + 2r

VI. CUBOID Volume of a cuboids =(l×b×h) cubic units Surface area=2(lb+bh+hl) Sq.units

Diagonal=√ l2+b2+h2 units

Area of 4 walls of a cuboid=2(l+b)×h sq.units

VII. CUBE

Volume= a3 cubic units

Surface Area= 6a2 sq. Units

Diagona=√3 a units

VIII. CYLINDER

volume=(π r2h) cubic units

Curved surface area= 2πrh sq. Units

TSA= 2 π r2+2πrh= 2πr(h+r) sq.units

IX. CONE

Slant height L=√h2+r2

Volume=13π r2h cubic units

Inoculate:- immunize, vaccinate, safeguard against

Curved Surface Area= πrl sq. Units

TSA=(πrl+π r2) sq. Units

X. SPHERE

Volume=43 π r3cubic units

Surface Area=(4π r2) sq. units

XI. HEMISPHERE

Volume=23 π r3cubic units

CSA=2 π r2 sq units

TSA= 2π r2 + π r2=3 π r2 sq units

Note: 1m3= 1000 litre

1000cm3 =1 litre

16. CLOCKS

Angle traced by minute hand in 60min= 360°

So angle made in min=36060 =6°

Every minute minute hand makes 6° angle

Angle traced by hour hand in 60 min=30°

so angle traced by hour hand in 1 min =3060=( 12 )

°

Every minute hour hand of a clock makes ( 12 )°

In 60 minutes, the minute hand gains 55 minutes on the hour hand.

17. PERMUTATIONS AND COMBITIONS

n!=n(n-1)(n-2)......3.2.1

e.g.: 6!= 6*5*4*3*2*1

Permutation: The different arrangements of a given number of things by taking some or all at a time, are called permutation.

No. of permutations= No of permutations of n things taken r at a time is

nPr=n!

(n−r )!

e.g.: 6P2=6!/4!=6*5*4!/4!=30

Peruse: - read or examine thoroughly or carefully, scrutinize, wade thorough

Combination: Each of the different groups or selection which can be formed by taking some or all of a number of objects is called a combination.

No. of combination: the no of all combination of n things, taken r at a time is

nCr= n !

r ! (n−r )!

Note: nCn=1 and nC0=1

e.g.: 11C4=11!/4!*7!=330

18. PROBABILITY

Probability is the measure of the like hood that an event will occur.

Probability is quantified as a number between 0 and 1. The higher the probability of an event, the more certain we are that the event will occur.

Probability P(E)= Favourable outcomeTotal possibleoutcome

Coin If a coin is tossed then total outcome=[H,T] If two coins are tossed then total outcomes = HH,HT,TH,TT For three coins total Outcomes=HHH, HHT, HTH, HTT, THH , TTH, THH, TTT If two dice is thrown then total possible outcomes=6×6=36 A pack of cards has 52 cards. There are 13 cards of each suit namely. Spades, clubs, hearts and diamonds. Spades and clubs are black cards. Hearts and diamonds are red cards. Aces, kings, queens and jacks are called face cards. So total no. Of face cards=4×4=16. Each card is 4 in number.

19. TRIGNOMETRY

h2=p2+b2

sinθ=ph cosecθ=

hp

cosθ=bh secθ=

hb

tanθ=pb cotθ=

bp

20. GEOMETRY

sum of total angles of a polygon= (n-2)180

so each angle of a polygonis equal ¿ (n−2)180n

Acumen: - the ability to make good judgements and take quick decisions, astuteness, shrewdness, canniness, sagacity

21. Series

Arithmetic Progression nth term Tn= a+(n-1)d

sum of n terms Sn= n2[2a+(n-1)d]

sum of n continuous terms starting from 1=n(n+1)2

Sum of first n even numbers= n(n+1)

Sum of first n odd numbers=n2

22. Quadratic equation

If ax2+bx+c=0 Then x=−b±√b2−4ac2a

23. MISCELLANEOUS

(a+b)2=a2+2ab+b2

a−b2=a2-2ab+b2

(a+b)2= a−b2+4ab

(a−b)2 ¿(a+b)2-4ab

a2−b2 = (a + b) (a-b)

(a+b)3=a3+b +3ab(a + b)

(a−b)3=a3-b3-3ab(a-b)

a3+b3= (a+b) (a2-ab+b2)

a3-b3=(a-b) (a2+ab+b2)

(a+b+c )2=a2+b2+c2+2ab+2bc+2ca

a3+b3+c3-3abc=(a+b+c) (a2+b2+c2-ab-bc-ca)

= 12[a+b+c] [(a−b)2+(b−c )2+(c−a)2]

If a +b +c=0, Then a3+b3+c3=3abc

If any number will fit in the form of (6k+1) or (6k-1) then number will be a prime number.

The difference between C.I and S.I for 2 years is

Diff=P( R100 )

2

Sum of all exterior angles of a polgon=360°

So one exterior angle of polygon of n side=( 360n

)

If n person are shaking hand with each other in a group then

Total no. Of handshake= n(n−1)2

Juggernaut:- extremely large and powerful, that cannot be stopped, a huge powerful and overwhelming force