27 Fastest Math Tricks

This Chapter covers;

1. Imaginary Number problems Trick

2. Prime Number Tricks-2
3. Addition Tricks, Subtraction Tricks(cross method)
4. Multiplication Tricks 2x2 trick
5. Multiplication tricks 3x2 trick.
6. Multiplication tricks same unit digit trick.
7. Multiplication tricks same 10th digit trick.
8. Multiplication tricks (unit + 10th digit = 10) trick.
9. Multiplication tricks 3x3 trick.
10. Multiplication tricks 4x4 trick.
11. Square Tricks in 10 secs/Square tricks in 30 sec.
12. Cube Tricks
13. Square root tricks,
14. Cube root tricks
15. Fraction tricks
16. Sum of natural numbers/sum of squares of natural no. formulae
17. Sum of even no./odd numbers tricks
18. Division, Remainders related Tricks
FT-1: Imaginary number Trick:
Q.1) Solve 3 4 ans.2-i

FASTEST BASIC TRICK-I

SOLVE IT BY TRICKS ALSO:

Divide 4i by 2 , which will give answer as 2i; now factorise 2i = 2 x i it means answer will be 2-i.,
- sign is taken between 2 and I, because, in question, between 3 and 4i, sign is -. If this would
have been + then we will take + sign and answer will be 2+i.

Practice Q.2)Solve 21 20 ans. 5-2i

Practice Q.3)Solve 5 + 12 ans. 3+2i

Some question is more hard, for e.g. Solve 5 + 12 ; here when 12i is divided by 2,
then we get 6i now factor of 6i are many,
We can take, 1x 6i or 2 x 3i or 3 x 2i, in such case, we solve (2) + (3i) = -5, but in
question 5 is at first place. Then do this calculation (3) + (2i) = 5, hence the correct factor
is 3 and 2i, then answer will be 3 + 2i.
Now Solve Q.4) Solve 32 + 24
Ans. 6+2i
Practice Q.3)Solve 5 12 ans. 3-2i

6.even numbers - divisible by 2 (e.g. 2,4,6,8,10,....... etc.)

7.Odd numbers - not divisible by 2 (e.g. 1,3,5,7,.....etc.)
8.Prime numbers a number which has no factors except one and itself. Prime number
starts from 2. (e.g. 2,3, 5,7,11,13,17....................etc.)
1 is neither prime nor composite number.
Prime number always starts from 2.
The only even prime no. is 2.
Composite number- which have factors other than 1 and itself.(e.g. 12,16,20
,....etc.)

Facts: Between 1 to 50, prime numbers are 15.

Between 51 to 100 , prime numbers are 10.
 Between 1 to 100, number of prime numbers is 25.
Between 70 to 100, how many prime numbers are ? ans.6

FT-2: Prime number Trick:

SOLVE By trick:

44-22-322-321 is the universal trick for getting no. of

prime numbers between any number to any number upto 100.

SOLVE By trick: Remember a tricky 10 digit number 4422322321

Between 1 to 10 there are 4 prime numbers (i.e. 2,3,5,7)
Between 11 to 20 there are 4 prime numbers (i.e. 11,13,17,19)
Between 21 to 30 there are 2 prime numbers (i.e. 23,29)
Between 31 to 40 there are 2 prime numbers (i.e. 31,37,)
Between 41 to 50 there are 3 prime numbers (i.e. 41,43,47)
Between 51 to 60 there are 2 prime numbers (i.e. 53,59)

Between 61 to 70 there are 2 prime numbers (i.e. 61,67)

Between 71 to 80 there are 3 prime numbers (i.e. 71,73,79)
Between 81 to 90 there are 2 prime numbers (i.e. 83,87)
Between 90 to 100 there are 2 prime numbers (i.e. 97)

Q.2: Between 30 to 70, how many prime numbers are ? ans.9

Since 30 is not a prime number, see prime numbers between 31 to 70 in following
table.

No.of 4 4 2 2 3 2 2 3 2 1
Prime
numbers
1 to 11 to 21 to 31 to 41 to 51 to 61 to 71 to 81 to 91 to
10 20 30 40 50 60 70 80 90 100

Ans. = 2 + 3 + 2 + 2 = 9 ans.
Prac. Q.) Between 20 to 70 how many prime numbers exist? Ans.11
( i{h : BE +{ ]E n E + +SU i
Z *V +{ ]E <i E i Mhx x E +
{{ { =k Ji VB* Ji Sj B E ]E
Zx E B nB MB *)

FT-1(FASTEST TRICK-1): Addition Trick:

Bank, PO, SSC +n v E< {I+ Vb(addition)v xx |x {U
Vi VxE Ex E Mi *
1) 5231-3487+7331 - 2896 + 2134 3728 = ?
vhi ={H E conventional method xi V Vn Mi *
Conventional Method: +5231 - 3487
+7331 - 2896
+2134 - 3728
+14696 -10111

AGAIN 14696
- 10111
Ans. = 4585
SHORT TRICK METHOD (cross method):
+ xx lb +{xB + E SB* BE i E + vx J* n +{ xx ] lb |C]
E nM i n E< Mh ] VBM* Ex + iV +BM* + B iV E +{ Jn
x VBM:
20 20 20
1) 5231-3487+7331 - 2896 + 2134 3728 = 4|-15|-12|-15
4| 5| 8 | 5 ans. 4585

1 -7 +1 -6 +4 -8 = -15 ans. = 20-15=5

Similarly, first take unit digits of all numbers and calculate.
Unit digit calculation: { E <E< +E * + { (+) Sx +E E Vbi VB il <x (-) Sx
+E E P]i VB* 1 -7 Ex { -6 +BM* -6 +1 Vb n * -5 +BM* < -6 Vbx { -11 +BM*
-11 +4 Vb n * -7 +BM* < -8 Vbx { -15 +BM* + S E =k xM] + * and -15 is
immediate less than 20, < 20 P]E 5 =k J n*
10th Digit calculation: + +M n< +E 2 E * + S E 20 P] <B +M n< +E 2 E
* n 10 P]i i 1 E i n 30 P]i i n< +E E 3 E i* x 5231 E 3 2 P]E 1 E
S* + 1 <x 8 -7M* <x 7 { 3 <x 4 M V +M <x 9 Vb E <x 13 nM*
 <x 13 { 3 <x 10 M V +M <x 2 Vb E <x 12 nM* < 20 P] n* + M 8
V =k n< lx { J n*
100th Digit calculation: + +M +E 2 2 E * + S E 20 P] <B +M +E 2 E *
x 5231 E 2 2 P]E 0 E S* + 0 <x 4 -4 M* <x 4 { 3 <x 1 M V +M
<x 8 Vb E <x 9 nM* <x 9 { 1 <x 8 M V +M <x 7 Vb E <x 15
nM* < 20 P] n* + M 5 V =k third lx { J n*
1000th Digit calculation: + +M +E 5 2 E * + SE 20 P] <B +M +E 2 E *
x 5231 E 5 2 P]E 3 E S* 3-3+7-2+2-3 =4
Example No.2 (BY SHORT TRICK)
2) 9716 - 4371 + 5053 3727 + 1813 = 8484

+6 -1 +3 -7 +3 = 6-1+3-7+3=4
Take 10th digits of all numbers as follows:
+1 -7 +5 -2 +1 = 1-7+5-2+1= -2 (10-2=8)

For 100th digits of all numbers, take following steps:

+6 (7-1) -3 +0 -7 +8 = 6-3+0-7+8= 4
+ SE 10 P] <B +M +E 1 E *
For 1000th digits of all numbers take following steps:
+9 - 4 +5 -3 +1 = 8
Example No.3 (BY SHORT TRICK)

3) 3.3 - 13.33 +31.13 - 13.31 + 1.3 = ? ans. 9.09

First take equal decimal digits and then apply aforesaid method:

3.30 13.33 + 31.13 13.31 + 1.30 = 9.09

Take Unit digits of all numbers:

0 -3 +3 -1 +0 = -1 (10-1=9), write 9 at 1st place of answer from
right side.
Take 10th digits of all numbers:
+2 (3-1) -3 +1-3+3= 0 write 0 at 2nd place of answer from right side.

<E< +E E =k -1+ l* V x 10 P]E 9 J l +i: + +M n< +E E Mhx {

digit E 1 E M*
(In solution of unit digits, we got the answer -1, then we subtracted it from 10 and write 9
as the answer. The effect of 10 will be taken as -1 from 10th digit.)
Take 100th digits of all numbers:3-3+1-3+1 = -1 (10-1= 9 will be taken at 3rd place of
answer from right side.)
Take 1000th digits of all numbers:
(In solution of 100th digits, we got the answer -1, then we subtracted it from 10 and write 9
as the answer. The effect of 10 will be taken as -1 from 10th digit.)

-2+3-1 = -1 (10-1= 9 will be takenat 3rd place of answer from right side.)
Example 4:

4323 1676 + 3421 - 5678 = ? - 2369 ans. 2759

Bring 2369 at left side and treat it as + 2369 then start calculation as example no.2.
4323 1676 + 3421 - 5678 + 2369 = ?
3 -6 +1 -8 +9 = -1
1 -7 +2 -7 +6 = -5
2 -6 +4 -6 + 3 = -3
3 -1 +3 -5 +2 = 2

PRACTICE QUESIONS : Solve the following questions by applying

aforesaid short trick.
1) 5231-2786+4563-3875 = ? ans. 3133
2) 6723-3778+5221-4882 = ? ans. 3284
3) 5321-3897+4225 =? + 2975 ans. 2674
4) 6821 - 4837 - 2895 = ? - 4425 ans. 3514
5) 6562-3998+5273-4867= ? ans. 2970
6) 56342-3768+457-39 =? Ans. 52992
7) 564.3-39.5+673.34-52.1+45.372 =? Ans.1191.412
8) 54.41 - 45.14+44.51 - 41.45+55.45 =? ans. 67.78
9) 5213.4-2734.67+3411.31-2963.53 =? ans. 2926.51
10) 4356 + 2398 4477 + 3322 = ? ans. 5599
If at the end last digit comes as -, then write it after nearest 10. and then subtract all from
hundredth, thousandth as the case may be.

For example:

If we dont know answer is in + or - , then what to do?

2723-3778+5221-5882 = ? (-2) 284

when comes -2, then subtract 284 from 2000 = 1716 ans.
 8 Multiplication Tricks:
FT-4(FASTEST TRICK-4):
General Trick: For any 2 digit- X 2 digit numbers Or 3 digit X 2 digit numbers:
45x67=? Or 68x 49 = ?, 127x 46 = ?, 167x 83 =?

Ex.2)45x67 = 4 5 a b
X
6 7 c d
----------------------------- ac | ad + bc | bd

4 X 6 (4x7) +(6x5) 5 X 7 Ans. Carry 6 3

30 1 5
(Start calculation always from right side : Calculate 5X7 =35, Write 5 in first column
and carry 3, Now do calculation of (4x7)+(6x5) =58 . Now add carrying digit 3 to it
that will give 58+3=61, write 1 in middle in answer column and carry 6. Now 4x6 =24.
Add carrying digit 6 , this will give 24+6=30. Write 30 in left column. Ans. Will be
3015. )
(nx i Ex E * Mh Ex E n <E< +E J + E carry E * V
|ii Mhx { 5 + 7 E Mhx M 35, +i: nx E 5 J + 3 carry
E* + (4x7)+(6x5) =58 + < carry 3 VbE 61 +BM* =k 1 J + 6 carry
E* + 4x6=24. + < carry 6 VbE 30 +BM ! 30 J* )
Practice Questions:
1) 64 x 38 = ?
2) 49 x 34 = ?
3) 86 x 56 = ?
4) 37 x 42 = ?
5) 48 x 64 = ?
Ans. 1) 2432; 2)1666; 3) 4816 ; 4) 1554;5)3072.
FT-5: 3 digit x 2 digit numbers: For eg. 127x 46 = ?. Take 12 as
unit place and do same calculation.

127x46 = 12 7

4 6
-------------------------------------

12 X 4 (12x6) +(4x7) 7 X 6 Ans. Carry 10 4

58 4 2
(Start calculation always from right side : Calculate 7x6 =42, Write 2 in first column
and carry 4, Now do calculation of (12x6)+(4x7) =100. Now add carrying digit 4 to it
that will give 100+4=104, write always unit digit i.e.4 in middle in answer column and
carry 10. Now 12x4 =48. Add carrying digit 10 , this will give 48+10=58. Write 58 in
left column. Ans. Will be 5842. )
( i{h : BE +{ ]E n E + +SU i Z *V +{ ]E <i E i Mhx x
E + {{ { =k Ji VB* ={ Ji Sj B E ]E Zx E B nB MB *)
Practice Questions:
1) 126 x 58 = ?
2) 143 x 78 = ?
3) 162 x 98 = ?
4) 137 x 64 = ?
5) 185 x 84 = ?
Ans. 1) 7308; 2) 11154; 3) 15876 ; 4) 8768; 5) 15540
FT-6: 2 digit x 2 same unit digit numbers: For eg. 87x 47 = ? or
58 x 98 = ?
Ex.1) 87 x 47 = 8 7

4 7
-----------------------------
8X4 (8+4)7 7 X 7 Ans. Carry 8 4
40 8 9
(Start calculation from right side : Calculate 7X7 =49, Write 9 in first column and
carry 4, Now do calculation of (8+4)7 =84 . Now 84 + 4 = 88, write 8 in middle in
answer column and carry 8. Now 8x4 =32. Add carrying digit 8 , this will give
32+8=40. Write 40 in left column. Ans. Will be 4089. )
Practice Questions:
1) 58 x 98 = ?
2) 67 x 47 = ?
3) 105 x 45 = ?
4) 183 x 53 = ?
5) 176 x 86 = ?
Ans. 1) 5684 ; 2 ) 3149 ; 3)4725; 4) 9699; 5) 15136
FT-7: 2 same 10th digit x 2 digit numbers: For eg. 87x 85 = ? or
52 x 59 = ?
Ex.1) 87 x 85 = 8 7

8 5
-----------------------------
8X8 8(7+5) 7 X 5 Ans. Carry 9 3
73 9 5
Practice Questions:
 1) 52 x 59 = ?
2) 67 x 64 = ?
3) 105 x 108 = ?
4) 93 x 95 = ?
5) 128 x 125 = ?
Ans. 1) 3068 ; 2 ) 4288 ; 3)11340; 4) 8835; 5) 16000.
FT- 8: 2 digit x 2 digit numbers: but condition is sum of unit
digits is 10, and 10th digits are same: e.g. 34x 36=?. 65x65 =?;
72x 78 = ?

Ex.1) 34x 36=3 4 x y

x z where y+z =10
3 6 x(x+1)| yz
-----------------------------

3 X (3+1) 4X6 Ans.

12 24

(Start calculation from right side :

Rule: always write double digit in right side. Calculate 4X6 =24, write 24 in first right
column. , Now do calculation of 3(3+1) =12 . Write 12 in left column. Ans. Will be
1224. Its very simple and user friendly )
(nx i Ex E * nx i n +E =k J * Mh Ex E n +E J V |ii
Mhx { 4 + 6 E Mhx M 24, +i: 24 J + + 3 E = BE fE x 4 Mh E n *
x 3(3+1)= 12, 12 J* Ans. Will be 1224.
Ex.2) 72 x 78 = 7x (7+1) | 2x 8 = 5616 ans.
Ex.3) 81 x 89 = 8(8+1) | 1 x 9 = 7209
n nx i Mhx Ex { <E< +E + i =E +M 0 M n* V ={H =nh 9 E
n =k 09 J n*
Ex.2)121x129 = 12 1

12 9
-----------------------------

12 ( 12 + 1) 1 X 9 Ans.
156 09
Practice Questions:
1) 45x45 = ?
2) 48x42 = ?
3) 76 x 74 = ?
 4) 93 x 97 = ?
5) 124 x 126 =?
Ans. 1) 2025; 2) 2016; 3) 5624; 4) 9021; 5) 15624
FT- 9: If unit digits are 5 and difference of 10th digits is 1 (one).
e.g. 85x 95=?. 65x75 =?; 35x 45 = ?

Ex.1) 85 x 95=8 5 x5 x y5 = ? where y>x.

9 5 = x (y+1) | 75
-----------------------------

lower X (higher+1) 75 = 8 ( 9+1) | 75. Ans. 80 75

Practice Questions:
1) 65x75 = ?
2) 35 x 45 =?
3) 95 x 105 =? 4)105 x 115 = ? 5) 55 x 65 = ?
Ans. 1)4875; 2)1575; 3)9975; 4)12075; 5)3575.
FT- 10: 3-digit x 3 digit General Trick: e.g. 385x 234=?. 432x654
In all bank exams, following questions are asked.:
Q. 23.4% of 385 = ? 9009.0/100 = 90.09 ans.
Q. 67.3 % of 549 = ? = 369.477 ans.
Q. 56% of 874 = ? = 489.44 ans.
Ex.1) 385 x 234= 3 8 5 a b c

2 3 4 d e f
------------------------------------------------- ad | ae+bd | cd+af+be|bf+ec|cf
3x2 3x3+2x8 3x4 + 2x5 8x4 + 3x5 5x4
+ 8x3

Ans. = 90090
(nx i Ex E * Mh Ex E n <E< +E J + E carry E * V
|ii Mhx { 5 + 4 E Mhx M 20, +i: nx E 0 J + 2 carry
E* + 8x4+5x3 E V 47 +BM < carry 2 E Vb E 49 +BM * + +M
E 9 J + 4 carry E * + Ex Ex Mh E + S Mh E = Vb* V
3x4 + 5x2+8x3 = 46 +BM*+ < E 4 Vb E 50 +BM* + 0 J + 5 E
E* + 3x3+8x2= 25 , + < carry 5 VbE 30 +BM*=k 0 J + 3 carry
E* + 3x2 + 3 =9 J* )

9 0 0 9 0
( Start your calculation from right side always. Only write unit digit and carry rest digits.
In multiplication of 385x234, multiply 5x4=20, write 0 in right end of column and carry 2.
Now do calculation as 8x4+5x3 (multiply and add in mind) = 47 . add carrying digit 2 to
it which will give 49, write 9 in 2nd right column and carry 4. Now do calculation 3x4 +
5x2+8x3 = 46 and add carrying digit 4 to it. Which will give 50, write 0 in third column 3
and carry 5. Now do calculation 3x3+8x2= 25. Add carrying digit 5 to it, which will give 30.
Write 0 in 4th column, and carry 3. No do calculation 3x2 + 3 =9.)
Q.3) 56% of 874 = ? = 489.44 ans.
FT-11; Tricks for 3 digit x 2 digits Multiplication:
Ex.1) 874 x 56= 8 7 4 a b c

0 5 6 0 e f
---------------------------------------- ax0 | ae+bx0 | cx0+af+be|bf+ec|cf
8x0 8x5+7x0 8x6 + 7x6 + 4x6
4x0 + 4x5
7x5
Ans. = 48944
-20-

(nx i Ex E * Mh Ex E n <E< +E J + E carry E * V

|ii Mhx { 4 + 6 E Mhx M 24, +i: nx E 4 J + 2 carry
E* + 7x6+4x5 E V 62 +BM < carry 2 E Vb E 64 +BM * + +M
E 4 J + 6 carry E * + Ex Ex Mh E + S Mh E = Vb* V
8x6+4x0+7x5 = 83 +BM*+ < E 6 Vb E 89 +BM* + 9 J + 8 E E*
+ 8x5+7x0= 40 , + < carry 8 VbE 48 +BM*=k 8 J + 4 carry E*
+ 8x0 + 4 =4 J* )

4 8 9 4 4

Practice Questions based on Tricks:

1) 123x 456 = ?
2) 345x 632 = ?
3) 786 x 456 =?
4) 893 x 673 = ?
5) 784 x 65 = ?
6) 453 x 86 = ?
7) 697 x 56 = ?
8) 45% of 876 = ?
9) 64.3% of 849 = ?
10) 4.5 x 3.7 x 5.6 = ?
Answers:
1) 56088 ; 2) 218040; 3) 358416; 4) 600989; 5)50960 ; 6) 38958; 7) 39032;
 8) 394.20 ; 9) 545.907; 10) 93.24
Solution of Q.10)First 4.5 x 3.7 = 16.65 ( do it by 2 digit x 2 digit General Trick)
Now 16.65 x 5.6
If problems of 4 digits x 2 digits come, then see the first two digit. If it is less
then 20 or it you know the table of it ( suppose it is 18, 25, 30, 10, 20, etc. in all
such cases, you know the table) . In present case first two digit is 16 , so do
calculation as follows:

16 6 5
0 5 6
---------------------
Now apply Trick FT-9.
16x0 16x5+6x0 16x6+5x0+6x5 6x6+5x5 5x6

93240 in answer, put decimal (.) after 3 last digit.

Now answer will be 93.240. after applying decimal rule.
Decimal Rule: See in 6.4x 1.2 = 7.68
(12x4= 48 write 8 carry 4. Now 12x6=72 . add 4 to 72 and get 76. Put decimal after
two digits because in question after one digit decimal come in 6.4 and also in 1.2
after one digit decimal come. )
But 6.4 x 0.12 = 0.768
FT-12: 4 digit X 4 digits Trick:

FT- 12: 4-digit x 4-digit General Trick: e.g. 7385x 6234=?.

In all bank exams, following questions are asked.:
Q. 23.45% of 6819 = ? ans. 1599.0555
Q. 764.3 % of 5492 = ? ans. 41975.356
.
2 3 4 5 a b c d

6 8 1 9 e f g h
---------------------------- ae | af+be |ag+ce+bf|ah+ ed +bg+fc|bh+fg+cg |ch+dg|dh

2x6 2x8+3x6 2x1 + 6x4 2x9 + 3x9+8x5+4x1 4x9+1x5 5x9

+ 8x3 6x5+3x1+4x8

Ans. = 1599.05.55
Practice Questions based on Tricks:
1. 5123x 3456 = ?
2. 7345x 6312 = ?
3. 7862 x 5416 =?
 4. 78.45% of 8761 = ?
5. 64.32% of 8493 = ?
Answers:
1)17705088 ; 2) 46361640; 3) 42580592; 4) 6873.0045; 5)5462.6976

FT- 13:
SQUARE TRICKS FOR 91 TO 99
91 = (91-9):(100-91) = 8281
(First make 4 columns of answer. Now subtract 91 from 100. It will give 9. Now
write 9 =81 in last two digits of column(suppose answer is unit digit such as 2=4
then write 04 . Now subtract 9 from 91, i.e. 91-9 = 82. Write it in first two columns
of answer.)
({ =k E S E xB* n 91 99 iE E M xEx i : { 100
91 P] n * 9 +BM * + 9 E M 81 M ( n B =k <E< J +B V 2
E M i 04 J n ) V E E nx i E n Jx J n* + 91 9
P]E x 82 =k E E B n Jx J n*)
97=97-3 | 3
9 4 0 9
Practice Questions:
i) 92 =?
ii) 94 =?
iii) 99 =?
iv) 96 =?
v) 98 =?
Answers: i) 8464; ii) 8836; iii) 9801 ; iv) 9216 ;v) 9604
FT- 14:
SQUARE TRICKS FOR 51 TO 59

51 = (25+1):(51-50) = 2601
2 6 0 1
(First make 4 columns of answer. Now subtract 50 from 51. It will give 1. Now
write 1 =1 in last two digits of column(suppose answer is unit digit such as 2=4
then write 04 . Now add 1 to 25. 25+1 = 26. Write it in first two columns of
answer.)
({ =k E S E xB* n 51 59 iE E M xEx i : { 51
50 P] n * 1 +BM * + 1 E M 1 M ( n B =k <E< J +B V 2
E M i 04 J n ) V E E nx i E n Jx J n* + 25 + 1
x 26 =k E E B n Jx J n*)
57=25+7 | 3 = 3249
3 2 4 9
Practice Questions:
i) 52 =?
ii) 54 =?
iii) 59 =?
iv) 56 =?
v) 58 =?
Answers: i) 2704; ii) 2916; iii) 3481 ; iv) 3136 ;v) 3316
FT- 15: (time 15 sec.)
SQUARE TRICKS FOR any Two digit number(38, 87 etc.

38 = x 2xy y

3 | 2x3x8 | 8 = 14 : 4 : 4= 1444 ans.

(First make 3 columns of answer. Now start calculation from right side.
8 will give 64. Write 4 carry 6. Now 2x3x8 = 48. Add 6 to 48 = 54. Wirte 4 in
answer and carry 5. Now 3 = 9 . add 5 to it. 9+5=14. Write 14 at left. )
67= 6 : 2 x 6 x 7 : 7
Carry 8 4
44 8 9
(Now start calculation from right side.7 will give 49. Write 9 carry 4. Now 2x6x7 =
84. Add carrying number 4 to 84 = 88. Wirte 8 in answer and carry 8. Now 6 = 36
. add 8 to it. 36+8=44. Write 44 at left. )
Practice Questions:
i) 82 =?
ii) 64 =?
iii) 79 =?
iv) 36 =?
v) 48 =?
Answers: i) 6724; ii) 4096; iii) 6241 ; iv) 1296 ;v) 2304
FT- 16: (time 25 sec.)
SQUARE TRICKS FOR any THREE digits number(136, 117 etc.
Apply same trick and take value of x=13, 11 etc.

136 = put x = 13 here.

x 2xy y

= 13 | 2x13x6 | 6 = 184 | 9 | 6 = 18496 ans.

OTHER QUESTIONS RELATED TO SQUARE TRICKS:
Q. ) 48 - 37 = ? ANS.935
Q. ) 78 - 67 = ? ANS.1595
Q.) 124 - 102 = ? ANS.4972
Q.)143 + 182 = ? ANS.53573
Q.) 47 + 53 = ? ANS. 5018
Q.) 98 - 94 = ? ANS.768
Q. ) 47 - 15 = ? ANS.1984
SBI ASSISTANT EXAM. 3.6.2014
Q. ) 106X106 + 94X94 =? ANS.20072
RRC HAJIPUR EXAM.10.6.2014

FT- 17: (time 30 sec.)

CUBE TRICK FOR any Two digit number(21, 24 etc.

21 = x xy X 3 xyX3 y

2 | 2x1x3 | 2x1x3 | 1 = 9261 ans.

(Illustration of Trick: start calculation from right side. 1=1, write 1 at
right side, carry 0. 3x2x1=6 , write 6 carry 0. 3x2x1= 12, write 2 carry 1.
2 will give 8 and add 1 to it then answer will be 9.)
24 =
x xyX3 xyX3 y

2 | 2x4x3 | 2x4x3 | 4 = 13824 ans.

Practice Questions:
i) 22 = ? iii) 23 = ?
ii) 31 = ? iv) 18 = ?
iv) 32 = ?
answers: i) 10648; ii) 29791 iii) 12167 iv) 5832 v) 32768
QUES. RELATED TO CUBE TRICKS
Q.29) 31 + 13 =? ANS.31988
30 ) 41 - 21 =? ANS.59660
31 ) 23 - 13 =? ANS.9970
FT-18: Trick for getting square root in 15 secs
(extremely fast trick)
In the following questions, we will learn , how to get square root of any number very fast
by tricky approach:
Q.1) 54756 =
23 4

23 6
54756 ans.234

(TRICK: { =k E n E xB* |x nB MB J E nx i { n +E E +b<x E

il +E E BE l (S n +E ix +E ) +b<x E n* 5 4 7 5 6 + +{ nJ E 1
E 9 E M Ex { E M E +i 6 +i * xSi { 4 6 E M Ex { 16 36 +i V
+i 6 * +i: =k 4 6 J =k E * + 547 E B nJ E EE M 547 E +i *
J 23 VE M 529 * n 24 E M M i 576 +BM V E 547 Vn * +i: =k E 23
J n * + =k i 234 M 236 * =k {x E B nJ E n M< J 547 EE xVnE b
J 576 U] J 529 E * xSi { +i xEx { {i M VBM* 547 U] J 529 E
xVnE +i: nx i U] +E x 4 6 4 +E +BM* +i: =k M 234 )
(Trick: underline 2 digits firstly and then underline all remaining digits as per given above.
Now for see only 6. 4 = 16, and 6=36. In each case, last digit is 6.
Choose both digits 4 and 6 for answer block. Now 23=529, 24=576. Since 576 is larger
than 547. Take 23 as answer. Now we have two options. 234 and 236. Now take
difference of 547-529=18 and 576-529=47. It means 547 is nearer to 529. (Since 547 is
nearer to smaller digit, take smaller digit 4 among 4 and 6 in right side. Answer will be 234.
)
Q.2) 21609 =
14 3
 14 7
Ans. 147
216 09
(TRICK: { =k E n E xB* |x nB MB J E nx i { n +E E +b<x E
il +E E BE l (S n +E ix +E ) +b<x E n* 2 1 6 0 9 + +{ nJ E 1
E 9 E M Ex { E M E +i 9 +i * xSi { 3 7 E M Ex { 9 49 +i V +i
9 * +i: =k 3 7 J =k E nx i * + 216 E B nJ E EE M 216 E +i *
J 14 VE M 196 * n 15 E M M i 225 +BM V E 216 Vn * +i: =k E 14
J n * + =k i 143 M 147 * =k {x E B nJ E n M< J 216 EE xVnE b
J 225 U] J 196 E * xSi { +i xEx { {i M VBM* 216 b J 225 E
xVnE +i: nx i b +E x 3 7 7 +E +BM* +i: =k M 147 )
(Trick: underline 2 digits firstly and then underline all remaining digits as per given above.
Now for see only 6. 4 = 16, and 6=36. In each case, last digit is 6.
Choose both digits 4 and 6 for answer block. Now 23=529, 24=576. Since 576 is larger
than 547. Take 23 as answer. Now we have two options. 234 and 236. Now take
difference of 547-529=18 and 576-529=47. It means 547 is nearer to 529. (Since 547 is
nearer to smaller digit, take smaller digit 4 among 4 and 6 in right side. Answer will be 234.
)
QUESTION RELATED TO SQUARE ROOT TRICKS:
32 ) 7744 = ? ANS.88
33 ) 2809 = ? ANS.53
34 ) 19321 = ? ANS.139
35. ) 38416 = ? ANS.196
36 ) 42025 + 55696 = ? ANS.21

37. ) 3969 = ? ANS.63

38. ) 8649 = ? ANS.93
SBI ASSISTANT EXAM. 03.06.2013
FT-19: Trick for getting Cube Root in 15 secs
(Firstly you remember following cubes to apply this trick:
1=1; 2=8; 3=27; 4=64; 5=125; 6=216; 7=343; 8=512; 9=729
In the following questions, we will learn , how to get Cube root of any number
very fast by tricky approach in only 10 sec:
3
1) 12167 = ? ans.23

2 3
12 167
(TRICK: { =k E n E xB* |x nB MB J E nx i { 3 +E E +b<x E
il +E E BE l (S n +E ix +E ) +b<x E n* 12 167 + +{ nJ E 1
E 9 E Cube Ex { E cube E +i 7 +i * xSi { 3 E cube Ex { 27 +i V
+i 7 * +i: =k 7 J =k E B i + 12 E B nJ E EE cube 12 E +i *
J 2 VE cube 8 * +i: =k M 23 )
(Trick: underline 3 digits of right side firstly and then underline all remaining digits as per
given above. Now for see only last digit 7. 3 = 27, write answer 7 in answer column.
Now see left two digit which is 12. Now think which cube will give less than 12. 2 will give
8 which is less than 12 . so write answer as 2 in left side of answer.
3
40 ) 39304 = ? ans.34
QUES. RELATED TO CUBE ROOT TRICKS
3
41 ) 103823 = ? ans.47
3
42 ) 54872 X (304 8) = (?) ans.38
IBPS PO EXAM. 17.6.2014
3
43 ) 2197 = ? ans.13

Q.1) if x = 6 + 6 + 6 + 6+. . . . , then find the value of x .

x
By Method: Since, this function is up to infinity, if you avoid first term, remaining
function also give value x.
What is factorisation rule:
By Method: let x = 6 + 6 + 6+. . . . quadratic equation is
2
ax + bx +c = 0 ;
Then x = 6 + ; x2 = 6+x; x2 x 6 = 0; Do axc; then take factors of
axc.
Now x2 3x + 2x 6 = 0; by factorization rule: 2
For example: 6x + 13x + 5=0
6X5=30 ka factorisation Karen;
x(x-3) + 2 (x-3)=0
30 = 10X3, 6X5 and 1X 30
(x-3) (x+2) = 0
x-3=0; x+2=0 Ab sabhi ko aapas me jode
ghata kar dekhen ki 13 aata hai
x=3; x=-2, negative value is discarded, ki nahi.
x = 3 ans. Now only 10, 3 ko jodne par 13
aatal hai. Now
2
6x + 13x + 5=0 ko aise likhen
2
6x + 3x + 10x + 5=0
3x(2x+1) + 5(2x+1)=0
Solution: By trick 21: it can be solved in 3 secs only. Take factor of 6 which has
Take (2x+1) common
difference 1. Factors of 6 are 1,6 and 2,3; Only 2& 3 factors
(2x+1) + have difference
(3x+5) =0; x=-1/2, -5/31.

6=2x3. Largest is the answer. Also dont touch pen.

Q.2) if x = 6 6 6 6. . . . , then find the value of x .

Trick: -22 First do factor of 6, i.e. 2,3 Here sign is so by trick answer will be
smaller number ans. will be 2.
Practice Questions:

Q.3) if x = 12 + 12 + 12 + 12+. . . . , then find the value of x .

Q.4) if x = 30 30 30 30. . . . , then find the value of x .

Answers: 3) 4 ; 4) 5;

Q.5) if x = 8 + 8 + 8 + 8+. . . . , then find the value of x .

In this question, factors of 8 are 1,8; 2, 4; no factors of 8 have difference 1. So

Solve by method as illustrated in Q.1 and apply following formula:

by comparing the equation with ax2 + bx + c= 0. You can get the

value of a , b and c

Then x = 8 + ; x2 = 8+x;
x2 x 8 = 0; by comparing the equation with ax2 + bx + c= 0. You can get the value
of a = 1 , b= -1 and c =-8
2 4 (1) (1)2 418
x= = = 3.3
2 21

1+4+1
By trick-23 : x = ; put n=8 here. And get the answer.
2

Practice questions;

Q.6) if x = 10 + 10 + 10 + 10+. . . . , then find the value of x .

Q.7) if x = 13 + 13 + 13 + 13+. . . . , then find the value of x .

4+1+1
(Hint: solve both Q.6 and Q.7 by using trick: x = )
2

Ans. Q.6) 3.7 ; Q.7) 4.14 ;

Q.7a.) if x = 10 10 10 10. . . . , then find the value of x .

4+11
(Hint: solve Q.7a. by using trick: x = )
2

Ans. 2.7
division : dividend = divisor x quotient + remainder
Q.8) If a number is divided by 18 the quotient is 215 and remainder is 11, find out the
number.
dividend (number) = divisor x quotient + remainder
Number = 18x215 +11 = 3881
ans.3881
Q.9) If a number is divided by 36 then remainder is 19. If that number is divided by
12, what will be the remainder?
Soln. since the number let x is divided by 36, it also be divided by its factor. 12 is
factor of 36. Now see only remainder now and divide remainder 19 by 12. Result
will be 7.
ans.7
Q.10) A divisor is 35 times of quotient and 4 times of remainder, if divisor is 420
then find out the dividend.
Use formula : dividend (number) = divisor x quotient + remainder
let remainder = x, then divisor = 4 x remainder.
420 = 4 x remainder; remainder = 105
Now divisor = 35 x quotient; now 420 = 35 x quotient; quotient= 12
Dividend = 420 x 12 + 105 = 5145
Q.25) In a two digit number the sum of digits is 6. If 18 is subtracted from the
number the digits are interchanged. find out the number.
By Method: let two digit number is xy. Where x is 10th digit and y is unit digit.
Then we know that number = 10x + y ; and given that x+ y = 6 ----------(i)
Now as per ques. 10x +y -18 = 10y + x ; 9x- 9 y = 18; x-y =2---------(ii)
Solving (i) and (ii), we get x = 4 and y = 2 .so number is 42.

Math without pen: Trick: -24

use eye only. Jo bhi number subtract hota hai. Jaise isme 18 is subtracted . then
divide 18 by 9 . result is 2 . take x-y=2 and x+y= 6 is given. Now solve both
equation in mind. Get x = 4 and y = 2. Ans.42
Q.26) In a two digit number the sum of digits is 12. If 54 is subtracted from the
number the digits are interchanged. find out the number.
ans.93
Solve it Math without pen technique. In 30 sec. only.
Practice Questions:
Q.27) In a two digit number the sum of digits is 12. If 36 is subtracted from the
number the digits are interchanged. find out the number.
Q.28) In a two digit number the sum of digits is 16. If 18 is subtracted from the
number the digits are interchanged. find out the number.
Q.29) In a two digit number the sum of digits is 9. If 45 is subtracted from the
number the digits are interchanged. find out the number.
Answers: 27) 84; 28) 97; 29) 72.

Q.30) If the product of two number is 4840, their ratio of 8:5, find the greatest
number. (based on pattern of SSC. Tier-2 exam. 2015)
Solution: take numbers as 8x and 5x. now 8x X 5x = 4840; then x = 11.
So greatest number is 8x = 8X11 = 88
Ans.88
Q.31) What should be added to 11216 to make it exactly divisible by 11?
A. 10 B. 1 C. 4 D.9
SSC Tier-1, 2013
Solution; take sum of odd placed digits and sum of even placed digits
1+2+6=9 (option B yahi par check kar len. Last digit 7 hoga. )
1+1 =2 now 9-2 = 7, it should be 0 or multiple of 11.
Now solve it by options:
First take option A.add 10, then 11216 + 10 = 11226
1+2+6= 9
1+2 = 3
Option C. Now add 4. 11216+4 = 11220
1+2+0=3
1+2=3. 3-3=0. So answer will be C.

Q.32) Find out a rational number between and .

A. 16/9 B. 9/16 C. 12/7 D. 7/3
SSC Tier-1, 2013
Soln. To find rational number between two fractions, denominators must be same.

Now multiply and means and

Rational number between 6/8 and 3/8 are 4/8, 5/8. But options have not the
answers.
62 32
Now take and i.e. 12/16 and 6/16;
82 82

Now take rational number between, 6/16 and 12/16.

i.e. 7/16, 8/16, 9/16,..11/16.
Choose from option, it is 9/16 ans.B.

Solve it by yourself: Q.33) Find out a rational number between and A.

1/5 B. 13/15 C. 11/15 D. 7/3
Ans.C
 Q.34

Solution: By Trick: -25

, Simply divide 18 by 17, this will give remainder 1. Ans.B

Q.35) The numerator of a fraction is 4 less than its denominator. If the numerator is
decreased by 2 and the denominator is increased by 1, then the denominator becomes
8 times the numerator, Find the fraction.
A. 4/8 B. 2/7 C. 3/8 D.3/7
SSC Tier-1, 2013
Solution: let denominator is x and numerator is x-4. Now given that
x-4 -2 and x+1, then x+1 = 8 X (x-4-2)
x+1 = 8x-48; 7x=49, x=7; so fraction will be x-4/x = 3/7 ans.D

Q.36) Find the simplest value of 250 + 18 72 .

(given 2 = 1.414)
A)10.312 B) 8.484 C)4.242 D)9.898

Soln. expression = 250 + 18 72 = 2252 + 92 362

= 102 + 3 2 62 = 72 = 7x 1.414 = 9.898 ans. D

Q.42) The numerator of a fraction is 1 less than its denominator. If the numerator is
decreased by 2 and the denominator is increased by 1, then the denominator becomes
double the numerator, Find the fraction.
A. 7/8 B. 6/7 C. 3/4 D.3/7

Q.43) Find the simplest value of 275 + 27 108 .

(given 3 = 1.732)
A)12.124 B) 10.124 C)21.241 D) 9.898

Answers: 38)b; 39) d ; 40) 2 ; 41) 2 ; 42) B; 43) A

Special series of fractions: Special Trick for it.

Sum of fractions starting from 1+

1
Q.1) 1+ ------------------ =?
1
1 + -----------
1
1+ ---------
7
TRICK-26 : remember a series start from 1, 2 and next is sum of
preceding two numbers:
Series is 1, 2, (1+2)=3, (2+3)=5, (3+5)=8, (5+8)=13, (8+13)=21
SERIES IS: 1, 2, 3, 5, 8, 13, 21,
+ + + + + + +

Now count how many + are in the question. In the above question,
we see that there are three +, so take only three numbers in
calculation 1,2,3
SERIES IS: 1, 2, 3, 5, 8, 13, 21,
+ + + + + + +
Trick -27 will be ( take x = 7 from question) = 3x + 2
---------- = 23/15 .
2x + 1

Practice question:
Q.2 ) 1
1+ ---- 1 = ? ans. 11/7
1+ ----------
1+ 1
 ---
3
Take another question, where there are five +

1
Q.3) 1+ 1
1+ 1
1+ 1
1+ 1
1+2

Here, Count no. of + it is 5 in the question no.3.

Now take up to five +
SERIES IS: 1, 2, 3, 5, 8, 13, 21,
+ + + + + + +

8+5 82+5
and make trick as = = = 21/13 ans.
5+3 52+3

Practice questions:
1
Q.1) 1+ 1
1+ 1
1+ 1
1+ 1
1+4

1
Q.2) 1+ 1
1+ 1
1+ 1
1+5

1
Q.3) 1+ 1
1+ 1
1+ 1
1+ 1
1+
1+1/9
answers:

1) 37/23 2) 28/17 3) 125/77

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