analytical skills building

Amity School of Business

Amity School of BusinessBBA, Semester IV

Analytical skills building


INTRODUCTION Number System Conversion:--

Binary: Base 2 system. Decimal: Base 10 system. Octal: Base 8 system. Hexadecimal: Base 16 system.


BINARY NUMBER SYSTEM The binary numeral system, or base-2 number system

represents numeric values using two symbols, 0 and 1.

Binary system is used internally by all modern computers.

The word Binary actually come from the Latin word bini, and means "two".

Binary digits are most often referred to as bits, short for "binary digits.“

Since binary is a base-2 system, each digit represents an increasing power of 2, with the rightmost digit representing 20, the next representing 21, then 22, and so on.


Decimal number system The Decimal numeral system (also called base ten) has

ten(10) as its base.

It is the numerical base most widely used by modern civilizations.

Decimal counting uses the symbols 0 through 9.


OCTAL NUMBER SYSTEM The Octal numeral system, or Oct for short, is the base-

8 number system.

It uses the digits 0 to 7. The main problem with binary numbers is that they take

up a lot of space. Octal is a shorter method of writing binary. Since the

octal base eight is a power of the binary base two ( 8 = 2³ )


In mathematics and computer science, Hexadecimal is a positional numeral system with base-16.

It uses sixteen distinct symbols, most often the symbols:-- 0–9 to represent values zero to nine, and, A- 10 B - 11 C - 12 D - 13 E - 14 F - 15

hexadecimal SYSTEM


CONVERSIONS CASE 1: Binary Decimal & Decimal Binary

CASE 2: Binary Octal & Octal Binary.

CASE 3: Binary Hexadecimal & Hexadecimal Binary.

CASE 4: Decimal Octal, & Octal Decimal.

CASE 5:Decimal Hexadecimal & Hexadecimal Decimal.

CASE 6: Octal Hexadecimal & Hexadecimal Octal.


DECIMAL BINARY OCTAL HEXADECIMAL0 0 0 0

1 1 1 1

2 10 2 2

3 11 3 3

4 100 4 4

5 101 5 5

6 110 6 6

7 111 7 7

8 1000 8

9 1001 9

10 1010 A

11 1011 B

12 1100 C

13 1101 D

14 1110 E

15 1111 F


TYPES OF NUMBER NATURAL: Numbers like 1,2,3,…..,smallest natural no. is

1 but there is no greatest number.

WHOLE: Numbers like 0,1,2,3…

PRIME: A number greater then 1, which contains only two different divisors, i.e., 1 or itself.

CO-PRIME: Two numbers a and b are said to be co-primes, if their H.C.F. is 1. e.g., (2, 3), (4, 5), (7, 9), (8, 11), etc. are co-primes

COMPOSITE: A number greater then 1 which contains more than two different divisors is 4,6,8,9…..


REAL: A number that can be written as a terminating or nonterminating decimal; a rational or irrational number.

RATIONAL: Each rational number is a ratio of two integers: a numerator and a non-zero denominator. Any repeating or terminating decimal represents a rational number. Since denominator can be 1, hence all integers are also rational no.’s.

IRRATIONAL: Irrational numbers include √2, π, and e. The decimal expansion of an irrational number continues forever without repeating.


SHORT-CUTS

22

2

2

)1(4

.'1

6

)12)(1(.'1

.1

.1

2

)1(.1

nn

snocubenstofSum

nnnsnosquarenstofSum

nnnoevennstofSum

nnooddnstofSum

nnnonaturalnstofSum


Factors and Multiples : If a number ‘a’ divides another number ‘b’ exactly, we say that ‘a’ is a factor of b. In this case, b is called a multiple of a.

Least Common Multiple (L.C.M.) : The least number which is exactly divisible by each one of the given numbers is called their L.C.M.

Factorization Method of Finding L.C.M.: Resolve each one of the given numbers into a product of prime factors. Then, L.C.M. is the product of highest powers of all the factors,

HCF & LCM


HCF & LCM Highest Common Factor (H.C.F.) or Greatest Common

Measure (G.C.M.) or Greatest Common Divisor (G.C.D.).

The H.C.F. of two or more than two numbers is the greatest number that divides each of them exactly.

There are two methods of finding the H.C.F. of a given set of numbers : Factorization Method: Express each one of the given

numbers as the product of prime factors . The product of least powers of common prime factors gives H.C.F.

Division Method: To find the H.C.F. of two given numbers. Divide the larger number by the smaller one


Formulas Product of two numbers =Product of their

H.C.F. and L.C.M.

H.C.F. and L.C.M. of Fractions:

atordenoofHCF

numeratorofLCMLCM

atordenoofLCM

numeratorofHCFHCF

min

min


DIVISIBILITY TEST Divisibility By 2 : A number is divisible by 2, if its unit's digit

is any of 0, 2, 4, 6, 8. Divisibility By 3 : A number is divisible by 3, if the sum of

its digits is divisible by 3. Divisibility By 4 : A number is divisible by 4, if the number

formed by the last two digits is divisible by 4. Divisibility By 5 : A number is divisible by 5, if its unit's digit

is either 0 or 5. Divisibility By 6 : A number is divisible by 6, if it is divisible

by both 2 and 3. Divisibility By 7 : Double the last digit and subtract it from

the remaining leading truncated number. Divisibility by 7 : Make pairs of 3 starting from right, add

all even and odd pairs together, then if the difference of sum of all odd pairs and all even pairs is either 0 or a multiple of 7.

Divisibility By 8 : A number is divisible by 8, if the number formed by the last three digits of the given number is divisible by 8.


Divisibility By 9 : A number is divisible by 9, if the sum of its digits is divisible by 9.

Divisibility By 10 : A number is divisible by 10, if it ends with 0.

Divisibility By 11 : A number is divisible by 11, if the difference of the sum of its digits at odd places and the sum of its digits at even places, is either 0 or a number divisible by 11.

Divisibility By 12 : A number is divisible by 12 if it is divisible by both 3 & 4.

Divisibility By 13 : Make pairs of 3 starting from right, add all even and odd pairs together, then if the difference of sum of all odd pairs and all even pairs is either 0 or a multiple of 13.

Divisibility By 14 : A number is divisible by 14, if it is divisible by both 2 and 7.

Divisibility By 15 : A number is divisible by 15, if it is divisible by both 3 and 5.

DIVISIBILITY TEST


Divisibility By 16 : CASE 1: If the thousands digit is even, examine the

number formed by the last three digits. CASE 2: If the thousands digit is odd, examine the

number formed by the last three digits plus 8. Divisibility By 17 : Subtract 5 times the last digit from the rest. Divisibility By 18 : A number is divisible by 18, if it is

divisible by both 2 and 9. Divisibility By 19 : Add twice the last digit to the rest. Divisibility By 20 : A number is divisible by 20, if it is

divisible by 10, and the tens digit is even. Divisibility By 20 : A number is divisible by 20, if the

number formed by the last two digits is divisible by 20.


PERCENTAGE Percent means hundredths.

E.g. ‘x’ percent means ‘x’ hundredths, & is written as x%.

To express x% as a fraction: We write, x% = x/100.

To express a/b as a percent: We write, a/b =((a/b)*100)%.


KEY CONCEPTS If A is R% more than B, then B is less than A by

:--[(R/(100+R))*100]%.

If A is R% less than B , then B is more than A by :-- [(R/(100-R))*100]%.

If the price of a commodity increases by R%, then the

reduction in consumption so as not to increase the expenditure is :-- [R/(100+R))*100]%.

If the price of the commodity decreases by R%, then the increase in consumption so as to decrease the expenditure is :-- [(R/(100-R)*100]%.


Let the population of the town be P now and suppose it increases at the rate of R% per annum, then : Population after n years =

Population n years ago=

Let the present value of a machine be P. Suppose it depreciates at the rate R% per annum, then: Value of the machine after n years =

Value of the machine n years ago =

nR

P

1001

nR

P

1001

nR

P

1001

nR

P

1001

nR

P

1001


PROFIT & LOSS COST PRICE: The price at which article is purchased.

Abbreviated as C.P. SELLING PRICE: The price at which article is sold.

Abbreviated as S.P. PROFIT OR GAIN: IF SP IS GREATER THAN CP.

(S.P.>C.P.) LOSS: IF SP IS LESS THAN CP. (S.P.<C.P.) Usually Gain or Loss is expressed as a percentage of C.P. MARKED PRICE: The price at which an article marked.

Abbreviated as M.P. Usually discount is offered at M.R.P., and the Discount=M.P.—S.P.


FORMULAES GAIN=(SP)-(CP).

LOSS=(CP)-(SP).

GAIN %=

LOSS%=

Discount=MP-SP

Discount%=

SPGain

%100

100

CPGain

100

%100

100CP

GainCP

Loss

100

%100

100CP

Loss

SPLoss

%100

100

SP=

SP=

CP=

CP=

If the article is sold at a gain of say 35%, then SP =135% of CP

If a article is sold at a loss of say 35%. Then SP=65% of CP

100MP

Discount


• If the trader professes to sell his goods at CP but uses false weights, then:--

• If the CP of two articles purchased is same. One of the two is sold at a gain of x% and the other is sold at a loss of x%, then on the whole there is no loss, no gain.

• If the SP of two articles is same. One of the two is sold at a gain of x% and the other is sold at a loss of x%, then there is always a loss, given as:-

%100

ErrorValueTrue

ErrorGain

100

100

%

2

2

xLoss

GainorLossCommonLoss


SPEED TIME & DISTANCE

hrkmmmhrkm

dsds

ddssisjourneywholetheinspeedaveragethethenhrkmsof

speedwithkmdanotherandsspeedaatdcediscertainaersmanaIf

hrkmyx

xyisjourneywholetheduringspeedaveragetheThenhrkmyat

cedisequalanandhrkmxatcediscertainaersmanaSuppose

aborba

iscedissametheertothemby

takentimestheofratiothethenbaisBandAofspeedstheofratiotheIf

TimeSpeedceDisSpeed

ceDisTime

time

ceDisSpeed

/5

18sec/1sec,/

18

5/1)5

)(:,/''

''''''tancov)4

/2

./

tan/tancov)3

:1

:1

tancov

,:)2

tan,tan

,tan

)1

2211

21212

211


RELATIVE SPEED

tstsDd

isdthemofbothbetweencedisttimeafterthenrespsswith

othereachtowardstimesametheatspodifferenttwofrommovingstartpeopletwoIf

tstsd

isttimeafterthembyeredcedisthethenrespspeedsswith

directionsametheintimesametheatposamefrommovingstartpeopletwoIf

tstsd

isttimeafterthemofbothbyeredcedisthethenrespspeedsswith

directionoppositetheintimesametheatposamefrommovingstartpeopletwoIf

vuspeedrelative

thenvuspeedswithdirectionsametheinmovemenobjectstwoIf

vuspeedrelativeaatothereachfromawayorothereachtowards

movingbetoseemtheythenresphrknvandhrkmuspeedsatothereach

fromawayorothereachtowardsdirectionsoppositeinmovingareobjectstwoIf

21

21

21

21

21

21

:)(tan,''.,''&''

int)5

:''covtan.,''&''

,int)4

:''covtan.,''&''

,int)3

,''&''/)2

.,/''/''

)1


CONCEPT OF TRAINS

.''

,/'','')5

.,/''

&/''''&'')4

.cov,,/''&

/'''''')3

.)(cov

''sin'')2

.''covtan

sinsin'')1

hrsu

yxlongkmy

bridgeapasstohrkmuofspeedaatmovinglongkmxtrainabytakenTime

hrsvu

yxothereachcrosstotrainsthebytakentimethenhrkmv

hrkmuatdirectionoppositeinmovingarekmykmxlengthoftrainstwoIf

hrsvu

yxtrainslowertheertotrainfasterbytakentimethenvuwherehrkmv

hrkmuatdirectionsametheinmovingarekmyandkmxlengthoftrainstwoIf

metresyxertotrainthebytakenTime

metresyofobjectstationaryagpasinlongmetresxtrainabytakenTime

metresxertotrainthebytakenTimemandingsa

orpoleaorpostgleagpasinlongmetresxtrainabytakenTime


.,,/''

./''&'')7

.,,/''

./''&'')6

vu

xmanthepasstotrainbytakentimethethentrainofoppositedirectiontheinhrkmv

ofspeedtheatmovingismanaIfhrkmuofspeedaatrunningislongkmxistrainAvu

xmanthepasstotrainbytakentimethethentrainofdirectionsametheinhrkmv

ofspeedtheatmovingismanaIfhrkmuofspeedaatrunningislongkmxistrainA


CONCEPT OF BOATS & STREAMS

hrkmudbstreamofSpeed

hrkmudawaterstillinmanboatofSpeed

hrkmbauupstreamSpeed

hrkmbaddownstreamSpeed

hrkmbstreamofspeedhrkmawaterstillinboatofspeedIf

UPSTREAMcalledisstreamtheagainst

directionDOWNSTREAMcalledisstreamthealongdirectionwaterIn

/)(2

1,

/)(2

1,/)3

/)(,

/)(,

/&,/)2

'.'

&'')1

Documents

analytical skills building