Quants Shortcut A4 -Prt
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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 1815 %NS. %NS . Ea),*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 Ea),*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 "%$("1 0tep ' "114 %NS S+tuat+o.2 ( &.e .u)ber +s 1 a. the other +s :1 Ea),*e ( 1&! x "# ( / 0tep 1 ' *! x # ( & 0tep 2' 1&!#(1&1 or "# * !(1&1 0tep ' 1&1&& & ( 1&&$& %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$1144
1 To square .u)bers e.+.< ;+th 5 Ea),*e ( 1&# ( 1 ( / Shortcut So*ut+o.( 1. Ta3e Ta3e the digit)s+ omitting omittin g # . 8ere it is 1&. 2. Ta3e the next number by adding 1 to the first. . ultiply both. 1& x 11 ( 11& 11& 4. insert 2# as last 2 digits to the product. 11&2#. %NS' %NS' 11&2#.
To f+. the ,rouct of 2 .u)bers c*ose to 1 S+tuat+o. 1( Both the .u)bers are 1 xample ' 1& x 1&# (/ 0tep 1' Write the numbers one below the other along with the excess over 1&&. 1
Ea),*e( 1&1#2 ( /
2. dd the 2 digits . "*%(1$ . 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 ( 178
1. digits omitting # ( 1&1 2. 1&1 x 1&2 ( )1&&*1+ x1&2 ( 1&2&& * 1&2 ( 1&&2 %NS( 1&&22#
Ea),*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$# ;0.
Ea),*e( "" > 11( / 1. " 2. "*" ( 1% . %" 4. "*1(1& # %NS( 189
Ea),*e( !$#! 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
Ea),*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 $! is divisible by 1". e.g.' 111(11* )2x1+ (1(1*)2x+( 1". 8ence 111 is divisible. 24 9f n is prime, greater than , n 2 - 1 is divisible by 24. 4% 9f n is even , n ) n2 * 2&+ is divisible by 4%
Shortcut So*ut+o.' 0ince the cost price is same, J of profit is same at 2#J. ;K WKA=9;L 90 AMN9A: T ??. ;0' d+ 2#J Ea),*e 2( Bananas bought at As.1& for 12 are sold at As.12 for 1&. What is the profit7loss J a+ #&J b+ 4%J c+ 4!J d+ 44J Shortcut So*ut+o.( 1& 12 12 B E
The solution for these type of problems is )BE - :+ 7: ( )12 x 12 1& x 1&+ 7 )1& x 1&+ ( 44. ;0' d+ 44J Ea),*e 3( The cost price of 1& bicycles is eGual to the selling price of % bicycles. What is the profit 7 loss J a+ 2&J profit b+ 2#J profit c+ 2&J loss d+ 2#J loss Shortcut So*ut+o.( @or every % bicycles sold, 2 bicycles is the profit. J of Hrofit ( )27%+ x 1&& ( 2#J ;0' b+ 2#J
#ER$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 ( $&&
!. Aeduced Hrice ( Aeduction in J 7 8ow much more for 1&&. !e. JS
Breath >J
%rea > U > JS
#r+ce >J
Dua.t+t> JS
Tota* E,e.ses > U > JS
J of
ales ( 47$ 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.(
Ea),*e1( others age is 4 times that of his son. # years bac3, it was $ times. What is mothers 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.' others 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 its not a multiple of $. ) 2%# ( 2 which is not a multiple of $+. . Kption E is the ;0WA 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 Ea),*e 2 ( 9n a lab for testing a petrolethanol 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/
Ea),*e 2 ( ?atha oined her first ob % years ago. 8er present age is !7# times her age at the time of oining the ob. ?athas sister was 1& years younger to her at the time of oining the ob. The age of ?athas 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
Ea),*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( ?athas age at the time of oining the ob is a multiple of #. Kption d - 4& is only a multiple of #. %NS ( d. Ea),*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 $.
Ea),*e3( 9n a village, 47$ 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
Ea),*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
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