Quants Shortcut A4 -Prt

Note about shortcuts 1& 1&#

There is no shortcut to all the types of problems in all the topics. Wherever shortcuts are available, we have furnished here with suitable examples.

0tep2' ultiply the excess

NUMBER SYSTEM

 x # ( 1#

0tep ' dd one of the 2 given numbers with the excess of the other number  1&* # ( 1&% or 1&# *  ( 1&%

By heart the following to speed up calculation. Square of 1 2 3 4 5 6 7 8 9 1 11 12 1 14 1# 1! 1$ 1% 1" 2& 21 22 23 24 25 26 27 28 29 Square of 3

* *#

1 4 9 16 25 36 49 64 81 1 121 144 1!" 1"! 22# 2#! 2%" 24 !1 4&& 441 484 529 576 625 676 729 784 841 9

0tep4 ' The product is obtained by 3eeping the number obtained in 0tep2 after the number obtained in step. i.e 1815 %NS. %NS . Ea),*e ( 1&" ( 1&" x 1&2 0tep 1' *" x *2 ( 1% 0tep 2 ' 1&"*2( 111 or 1&2*"(111 0tep ' 1111% %NS S+tuat+o.2 ( Both the .u)bers are : 1 Ea),*e( " x "% ( /  s in the above above step , deduct deduct the excess of of the other number from the first number and proceed . 0tep 1 ' $ x 2 ( *14 0tep2 ' " - 2 ( "1 or "%$("1 0tep ' "114 %NS S+tuat+o.2 ( &.e .u)ber +s  1 a. the other +s :1 Ea),*e ( 1&! x "# ( / 0tep 1 ' *! x # ( & 0tep 2' 1&!#(1&1 or "# * !(1&1 0tep  ' 1&1&&  & ( 1&&$& %NS  2 5eroes are added ta3ing account of signs6

MU!T"#!"$%T"&N S'&RT $UT( MU!T"#!"$%T"&N MU!T"#!"$%T"&N Mu*t+,*+cat+o. b- 5 or ,o;er of 5( ultiply by 1& and its powers and dividing by 2 and its powers. e.g.' 1! x # ( 1! x )1&72+ ( 1!&72 ( !%& e.g.' 11$# x !2# ( 11$# )1&72+ 4 (11$#&&&&71!

S'&RT $UT( MU!T"#!"$%T"&N MU!T"#!"$%T"&N To )u*t+,*- .u)bers c*ose to 1/1/ 1 ,.. say %,",11,"%, "", 1&1, """, 1&&1 ,.. $o.0ert $o.0ert the .u)ber .u)ber +.to 1  ./ .1/2/3/ .1/2/3/ a. ,erfor) the )u*t+,*+cat+o. e.g.' 12! x 1 ( 12! x )1&*+ ( 12!& * $% ( 1!% e.g.' " x "% ( " x )1&&2+ ( "&& - $% ( %22 e.g.' 2#! x ""%"" (2#! x )1&&&&& - 1&1+ (2#! x1&&&&&  2#! )1&& *1+ (2#! x1&&&&&  2#! x1&& 2#!   (2#2$1144

1 To square .u)bers e.+.< ;+th 5 Ea),*e ( 1&# ( 1 ( / Shortcut So*ut+o.( 1. Ta3e Ta3e the digit)s+ omitting omittin g # . 8ere it is 1&. 2. Ta3e the next number by adding 1 to the first. . ultiply both. 1& x 11 ( 11& 11& 4. insert 2# as last 2 digits to the product. 11&2#. %NS' %NS' 11&2#.

To f+. the ,rouct of 2 .u)bers c*ose to 1 S+tuat+o. 1( Both the .u)bers are  1 xample ' 1& x 1&# (/ 0tep 1' Write the numbers one below the other along with the excess over 1&&. 1

Ea),*e( 1&1#2 ( /

2. dd the 2 digits . "*%(1$ . 9nsert the last digit of the product as the last but one digit. ?ast digit is $ . 8ence $%. 4. add 1 to the first digit of the number and insert as the first digit. @irst digit is ". "*1(1&. inserting 1&$% %NS ( 178

1. digits omitting # ( 1&1 2. 1&1 x 1&2 ( )1&&*1+ x1&2 ( 1&2&& * 1&2 ( 1&&2 %NS( 1&&22#

Ea),*e ( $" x 11 ( / 1. " 2. $*"( 1! . !" 4. $*1 ( % #. ;0 %!"

Shortcut( To )u*t+,*- b- 25 1. 9nsert 2 5eroes on the right of the given number 2. Then divide it by 4 xample' #!$ x 2# ( / 0tep 1 ' 9nsert && to the right. #!$&& 0tep 2' :ivide by 4 ' #!$&&74 ( 141$# ;0.

Ea),*e( "" > 11( / 1. " 2. "*" ( 1% . %" 4. "*1(1& # %NS( 189

Ea),*e( !$#! x2# ( / 0olution'

!$#!&&74 ( "1%"&& ;0.

Shortcut( To )u*t+,*- b- 125

S+tuat+o. 3( The .u)ber has )ore tha. 2 +

2, 1, 1, 1,

 , 1&  , # 1 , # 1, 1

?E (  x  x 2 x  x # ( 2$&

xample' @ind out the no.of 5eroes in 2$F

#R&?"T @ !&SS ;o.of 5eroes (

27 5

 *

27 5

Ea),*e1( 2 pens are sold for As.#&. Hrofit earned is 2#J. What would be the profit if 4 pens are sold for As.1&&. a+ 1&J b+ 1#J c+ 2&J d+ 2#J

2

( # * 1 ( ! 5eroes %NS #&"NTS T& REMEMBER ( "C"S"B"!"TY 2 9f n is even or    The last digit of n is & or divisible by 2.  9f the sum of the digits of n is divisible by . 4 9f the last 2 digits of n is divisible by 4 # 9f the last digit is & or # ! 9f n is divisible by both 2 and . n )n*1+ )n*2+ is divisible by !. % 9f the last  digits of n is divisible by % " 9f the sum of the digits of n is divisible by " 1& 9f the last digit of n is & 11 9f the difference between the sum of digits in odd positions and the sum of digits in the even position is & or a multiple of 11. e.g.' 4$1". 4*1 ( #R $*"(1!. 1!#(11 is multiple of 11. 8ence divisible by 11. 12 ll numbers divisible by  and 4 are divisible by 12 $,11,1 9nteger n is divisible by $,11 or 1 if and only if the difference of the number of its thousands and the remainder of its division by 1&&& is divisible by $,11 or 1. e.g.' !!### divisible by $/ !!###(1%". 1%" is divisible by $. 8ence the number is divisible by $. 1" 9f the sum of the number of tens and twice the units digit is divisible by 1". e.g.'$! ( $ * )2 x !+ (1". 8ence $! is divisible by 1". e.g.' 111(11* )2x1+ (1(1*)2x+( 1". 8ence 111 is divisible. 24 9f n is prime, greater than , n 2 - 1 is divisible by 24. 4% 9f n is even , n ) n2 * 2&+ is divisible by 4%

Shortcut So*ut+o.' 0ince the cost price is same, J of profit is same at 2#J. ;K WKA=9;L 90 AMN9A: T ??.  ;0' d+ 2#J Ea),*e 2( Bananas bought at As.1& for 12 are sold at As.12 for 1&. What is the profit7loss J a+ #&J b+ 4%J c+ 4!J d+ 44J Shortcut So*ut+o.( 1& 12 12  B E

The solution for these type of problems is )BE - :+ 7: ( )12 x 12  1& x 1&+ 7 )1& x 1&+ ( 44.  ;0' d+ 44J Ea),*e 3( The cost price of 1& bicycles is eGual to the selling price of % bicycles. What is the profit 7 loss J a+ 2&J profit b+ 2#J profit c+ 2&J loss d+ 2#J loss Shortcut So*ut+o.( @or every % bicycles sold, 2 bicycles is the profit. J of Hrofit ( )27%+ x 1&& ( 2#J  ;0' b+ 2#J

#ER$ENT%AES 1. To calculate 1J of any given number, put a decimal before the 2 nd last number. e.g.' 12# x 1J ( 1.2#

xample' @ind out the no.of 5eroes in 1$F 137 5

137 +

5

2

1& :

137 +

5

2. To calculate 1&J of any given number, put a decimal before the 2 nd last number. e.g.' 12# x 1&J ( 12.#

3

( 2$ * # * 1 (  5eroes %NS

. To calculate 2#J of any given number, first divide the number by 2 O again divide the result by 2. e.g.' 2&& x 2#J ( 2&&72 ( 1&& O 1&&72(#&. ;0'#&

Short cut )etho us+.< factor+sat+o. to f+. !$M a+ :ivide each of the given numbers by prime factors till all the Guotients become 1 b+ Hroduct of all prime factors is the ?E

4. To calculate  P7Q J of any given number, divide the number by .. e.g.' 24& x  P7Q J ( 24&7 ( %&. ;0'%&

xample 1' ?E of 1%, 2$, & #. To calculate #&J of any given number, divide the number by 2.

 I1% , 2$ , &  I ! , " , 1& 3

e.g.' 1#& x #&J ( 1#& 7 2 ( $#. ;0' $#

of the males are married, then what is the unmarried females/ Shortcut So*ut+o.(  ssume that the population ( $&&

!. Aeduced Hrice ( Aeduction in J 7 8ow much more for 1&&. !e. JS

Breath >J

%rea > U > JS

#r+ce >J

Dua.t+t> JS

Tota* E,e.ses > U > JS

J of 

ales ( 47$ x $&& ( 4&& , @emales( $&&4&&(&& arried ales ( #J ;o.of ales arried ( 4&& x #J ( 14& ;o.of females married also ( 14& Nnmarried females ( &&14& ( 1!&

Nu)ber 1 >J >JS

Nu)ber 2 >JS >J

Nu)ber 1 >J >JS

Nu)ber 2 VJ VJS

%.s;er   >.> JS >.> JS

Total @emales && 1&&

%.s;er   > * V * )>V71&&6 J >  V  )>V71&&6 JS

3

 J

Nnmarried females J in population( # 1

3

 J

%AE #R&B!EMS

$o.0e.t+o.a* So*ut+o.(

Ea),*e1( others age is 4 times that of his son. # years bac3, it was $ times. What is mothers age/ a+ 2% b+ # c+ 4& d+ 4#

 ssume business ( 1&&. Hrofit (1&J , 9ncome (1& ;ew 9ncome ( 2#J ( 2# x >71&&

Shortcut So*ut+o.' others age is 4 times now # years bac3, it was $ times.

But 2# x >71&& ( 0ame 9ncome as received earlier  2#71&& > ( 1& R > ( 1& x 1&&72# ( 4&

1. Kption b and d are not multiples of 4. 2. Kption a is a multiple of 4 but # years bac3 its not a multiple of $. ) 2%# ( 2 which is not a multiple of $+. . Kption E is the ;0WA as 4& is a multiple of 4 and # years bac3 4&#(# is a multiple of $. %NS( $

arlier Business ( 1&&, ;ow Business ( 4&  J :own in business ( !&J ) 1&&4&+71&& down Shortcut So*ut+o.( )2#J  1&J+ 7 2#J ( )# - 2+ 7 # ( 7# ( !&J Ea),*e 2 ( 9n a lab for testing a petrolethanol engine, the fuel tan3 is filled up fully with pure petrol. 1&J is replaced by ethanol and the process is repeated thrice. t the end of the third operation, what is the J of petrol/

Ea),*e 2 ( ?atha oined her first ob % years ago. 8er present age is !7# times her age at the time of  oining the ob. ?athas sister was 1& years younger to her at the time of oining the ob. The age of ?athas sister is

Shortcut So*ut+o.( Total 1&&

Hetrol 1&&1&("&

thanol 1& ) total to be 1&&+

1&&

"&" ( %1 )"&x1&J(" is removed+

1")s total to be1&&+

%1 - %1x1&J (%1 %.1($2."

2$.1 ) 1&&$2."+

1&&

1!& >

> ( )1!& x 1&&+ 7 && ( # 1

Ea),*e 1( The income of a shop remains unchanged though the profit is increased from 1&J to 2#J. What is the J of down in business /

 

Nnmarried females

a+ 2

b+ !

c+ %

d+ 4&

Shortcut( ?athas age at the time of oining the ob is a multiple of #. Kption d - 4& is only a multiple of #. %NS ( d. Ea),*e 3( Ten years ago  was half of B in age, if the ratio of their present ages is '4, what is the sum of their present ages/ a+ % b+ 2& c+ # d+ 4#

%NS( J of petrol at the end of the process($2."J

Shortcut(  ges are in the raio of  and 4 i.e in multiples of  and 4. 0o sum of their ages should be multiple of $.

Ea),*e3( 9n a village, 47$ part of the population is males. 9f #J

4

Kption c is # which is a multiple of $. %NS' c.

increase by &.#. What is the weight of the teacher/ Shortcut( ;o.of values ( # * 1 ( 9ncrease in average ( &.# 9ncrease in total value ( ! x &.# ( 1%. Weight of the teacher ( 4% *1% ( !!.

!.

%NS

Ea),*e 5( The average wages of a wor3er during a day comprising 1# consecutive wor3ing days was As."1 per day. :uring the first $ days, his average wages was As.%% per day and the average wages during the next $ days was As." per day. What was his wage on the 1#th  day/

%CER%AES 9f there are n values and one value is added, the average will increase7 decrease and the total value will also increase7decrease . ".crease +. a0era