GAT a Formula List

8/18/2019 GAT a Formula List

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GAT A

FORMULA SHEET

Math Topics

Age problems

Work hours problems

Clock agles a! Sector area

Algebraic e"pressios

Spee! !istace problems

Fractios # $ercetages

Rage% mea% Mo!% Me!ia

Simple Geometr& problems

'asic Arithmetic

$robabilit&

Ratios

$ro(it% )iscout problems

E*uatio sol+ig (or ,ariables


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'asic Calculatios

S*uare% Marble Si-e

'ri!ge Legth

Fractio 'ase! Gai% Loss

Fi!ig Share

./Mea

The mean average is not always a whole number.

The mean is the total of the numbers !i+i!e!byhow many numbers there are.

To work out the mean:

1. Add up all the numbers.7 + 9 + 11 + 6 + 1 + 6 + 6 + + 11 ! 7"


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". #ivide the answer by how many numbers thereare.There are 9 numbers.

7" $ 9 ! %So the mea +alue is 0/

12 Mo!e

The mode is the value that appears the most.

7 9 11 6 1 6 6 11

To work out the mode:

1. &ut the numbers in order: 3 3 3 7 9 11 11 1

". 'ook for the number that appears the most.

6 appears more than any other number.So the mo!e +alue is 3/

4/Me!ia

The median is the mi!!le value.

To work out the median:



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". The number in the middle of the list is themedian.So the me!ia +alue is 5/

(f there are two middle values) the medianis hal(6a& between them. *ork out the median forthis set of numbers:

6 6 6 5 0 9 11 11 1

There are two middle values) 7 and %.

The median is hal(6a& between 7 and %) so themedian is

7/Rage

The range is the !i((erece between the biggestand the smallest number.

To work out the range:


". ubtra,t the smallest number from the biggestnumber:

1 - ! 1So the rage o( this set o( umbers is .8.

9/Sum o( Series


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um of an series !

/0p.what is the avg of first " multiples of 7

7)12)"133.12

um!447+125"5"

um!7.8"

*e have to find avg so

Avg!7.8""!7.8 ans

3/$robabilit&Ten ,oins are tossed simultaneously. (n how many of the out,omes will the third ,oin turn up a head

A. "1

. "9

. "%

#. "9

/. ;one of these

The ,orre,t ,hoi,e is 45 and the ,orre,t answer

is 1:.


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(f two di,e are thrown what is the probability of

soming a sum of 9.42)85348)253.4)653..46)5 Total 2 ways to be,ome

9

o 26!19 ans


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!9=8=49-85=!1"6

:2MAR'LE S;=E

?arble si@e is ",m,m. >ow many marbles arereuired to ,over a suare with side m

m!,m

Area!

Area?Marble si-e

!"!18

.12 LE


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*hat is the number more than the double of

spe,ifi, value of 0..

"0-imilarly3.

*hat is the number less than the double of

spe,ifi, value of 0..

"0+

.42LOG $RO$ERT;ES

'og40.y5!log 0+logy

'og40y5!log0-log y

ln e!1

ln 0B"!"ln 0

.72 Clock Agles Angle tra,ed by hour hand in 1" hrs ! 6C. Angle tra,ed by minute hand in 6 min. ! 6C.

8:8 .. e0press hour hand in degree

As 1"e,tors on ,lo,k!6 degree

8+86!18+17.8!167.8


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.72WORB SHARE

Amount of *orkTime!Dutput4Eate5

A ,an do a pie,e of work in 2 hoursF and

together ,an do it in hours) while A and together

,an do it in " hours. >ow long will alone take to do

it

A!12

+!1

A+!1"

!1"-12!12

!1-12!11"

o alone will do in 1" hours

.92 AREA # C;RCUMFERE


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.32 AREA OF SUARE%triagle%rectagle

Area of suare! sB"

&erimeter!2s

Area of triangle! bh"

&erimeter! sum of all sides

Area of /uilateral triabgle!srt sB"2

&erimeter!s

Area of re,tangle! '*

&erimeter!"4'+*5

Golume of ,ylinder ! pirB"h

Golume of ,ube!aBir,umferen,e of a ,ir,le ! "HE.(5. ir,umferen,e of a semi-,ir,le! HE.((5. Area of semi-,ir,le ! HE" ".


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Cube :Let each edge of a cube be of length a. Then,1. Volume = a3 cubic units.2. Surface area = 6a2 sq. units.3. Diagonal = 3a units.

Cylinder :Let radius of base = r and !eight "or length#= h. Then,1. Volume = "$r2h# cubic units.2. %ur&ed surface area = "2$rh# sq. units.3. Total surface area = 2$r"h ' r# sq. units.


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.52 i +alues

(!srt of -1

(B"!-1

(B2!1

.02

A+erage (ormula2

'et a1)a")a)......)an be a set of numbers) average !

4a1 + a" + a)+......+ an5n

Average! sum of elementsno of elements

.:2 RAT;O

:b!0:,I!

,!b0


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I!,b

182 Algebra

aBnaBm!aBm+n

aBnaBm!aBn-m

.:2

(f Jiven #ata is

&assed in 1st sub!0K.......&ass in "nd sub!y

K......failed in both sub!@K

Then we ,an find K of passing students in both sub

by this formula

passed in both K! passed in 1st sub+passed in "nd

sub+failed in both-1K.

imilarly

(f given data is


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Then we ,an find K of students failed in both sub by

this formula


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1!""

!""

is the per,ent share of ,heapest mobile

Total!1+1"8+""8!28

""8!8K

1+1"8!""8!8K

18""8!"".""K

Simple Interest (S.I.) :(f the interest on a sum borro)ed for certain*eriod is rec+oned uniforml, then it iscalled simple interest.Let the principal = P, Rate = R% per annum

(p.a) and Time = T years. Then ,

1. S.I. = (P x R x T / 1)!. P = (1 x S.I. / R x T)

". R = (1 x S.I / P x T)

#. T = (1 x S.I. / P x R).


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112 S;M$LE EU TO F;


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>ow mu,h speed of train must be in,reased if time

is redu,ed by "K 3

!vt3.suppose s!1) t!1G!11!1

"K les time!1-"!%

G!1%!1".8

1".8-1!".8 hen,e "8K

192

'argest of 1 ,onse,utive intgrs whose sum is

-6 to 6

'argest !6

'eat no of among three digits whose sum is 1%!

8..b,@

I+I+1+I+"!1%333333I!18I!8333

8+6+7!1%

132 Sum O( Series2

n!n4a1+an5"

/0ample. um of numbers from 1)")33..1 a1!1Fan!1


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n!1n!141+15"!88

152 Gai% Loss


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'oss &er,entage: 4'oss K5'oss K ! 4'oss 0 1 .& 5

102 $ercetage2on,ept of &er,entage :y a ,ertain per,ent) we mean that many

hundredths. Thus) 0 per,ent means 0 hundredths)written as 0K.(. To e0press 0K as a fra,tion: *e have) 0K ! 0 1.Thus) 2%K ! 2% 1 ! 1" "8.((. To e0press a b as a per,ent :*e have a b ! 4a b O 15K.

&er,ent to fra,tion: 0K ! 01

&er,entage formula: Eate1 ! &er,entagebase

'oss ! 4.&.5 - 4.&.5.Jain &er,entage: 4Jain K5Jain K ! 4Jain 0 1 .&5


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Properties of Logarithms :1. loga"-# = loga - ' loga 2. loga"- # = loga - / loga

3. log- - = 10. loga 1 = . loga "-*# = *"loga - #6. loga - = 1 log-a

Some Important Formulae :(. " 1 ' 2 ' 3 ' .....' n# = n "n ' 1 # 2((. "1 2 ' 22 ' 32 ' ..... ' n2# = n " n ' 1 #"2n ' 1# 6(((. "1 3 ' 23 ' 33 ' ..... ' n3# = n2 "n ' 1#2 0

Fractios (ormulas2


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Cosumer math (ormulas2

#is,ount ! list pri,e O dis,ount rate

ale pri,e ! list pri,e P dis,ount

#is,ount rate ! dis,ount $ list pri,e

ales ta0 ! pri,e of item O ta0 rate

(nterest ! prin,ipal O rate of interest O time

Tips ! ,ost of meals O tip rate

ommission ! ,ost of servi,e O ,ommission rate

Q

;aini Agha


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