Vedic maths is the ancient India secret before the calculator to fast calucation with short cuts and tricks for fast easy accurate answers. GRE exam and other competative exam test students on theability to solve the complex numercials problems with efficiently and within time limits. Vedic maths helps with tricks just for same. GREKing helping students in basic concepts. GREking the best GRE preparation classes in Mumbai. (www.greking.com)

1. Target 320+ in GRE
1
GREKing

2. Vedic Numbers

3.  Number Tree
 LCM HCF
 Divisibility Rules
 Power cycle
 Remainder Theorem
 Remainder of powers an – bn
 Last and Second last digit
 Power of Exponents
 Euler’s Theorem
 Fermet’s Theory
 Wilson Theorem
 Number Systems (decimal binary)

4. Importance in exams
CAT – 4 questions
CMAT – 2 questions
NMAT – 5 questions

5. Number Tree

7. HCF & LCM

8. 42 = 21 x 2
= 7 x 3 x 2
• Factorize the following numbers:
• 42
• 72
• 84
• 65
• 108
• 210

9. • Calculate the LCM and HCF
for the following groups of
numbers
a) 42, 70
b) 18, 24, 60 ,150

10. LCM of nos 60
• Three bells ring after 3, 4 and 5 minutes
respectively. If they start ringing together, when
• will they ring together again?.
a) 50
b) 90
c) 60
d) 42

11. HCF of nos 10
• Three buckets of milk having capacities 40, 30 and 50 L
respectively. What is the largest
• size of the measure that can be used to pour milk from all
three buckets such that the
• volumes of milk contained in each bucket is an integral
number of pourings used by the
• measure.
a) 50
b) 10
c) 60
d) 42

12. A = 12 x
B = 12 y
144 xy = 2880
xy = 20
1, 20
2, 10
4, 5
5,4
10,2
20,1
• The product of two numbers is 2880. If the
HCF is 12, how many such pairs of number are
possible?
a) 3
b) 6
c) 8
d) 2

13. LCM of nos
720
• Find the least number which when divided by
9,12,16,30 leaves in each case a
• remainder of 3.
a) 721
b) 722
c) 723
d) 754

14. LCM of nos 15
105
120
135…..
• Find the number of all the numbers divisible
by 3 and 5 between 100 to 200.
a) 9
b) 8
c) 6
d) 7

15. M(3) + M(5) – M(3,5)
30 + 20 – 7
= 43
• Find the number of all the numbers divisible by
3 or 5 between 100 to 200.
a) 25
b) 89
c) 60
d) 43

16. LCM of nos 15
105
120
135…..
Sn = n/2 (a+l)
• Sum of all the numbers divisible by 3 and 5
between 100 to 200.
a) 1050
b) 8090
c) 6020
d) 4231

17. 120
• What is the least three digit number that is
divisible by 5 and 6?
• - What is the least 4 digit number that is
divisible by 12 and 15?
• - What is the least 4 digit number that is
divisible by 25 and 30?

18. Rules of Divisibility

19. TESTS OF DIVISIBILITY:
• Divisibility By 2 : A number is divisible by 2, if its unit's
digit is any of 0, 2, 4, 6, 8.
• Ex. 84932 is divisible by 2, while 65935 is not.
• Divisibility By 3 : A number is divisible by 3, if the sum
of its digits is divisible by 3.
• Ex.592482 is divisible by 3, since sum of its digits = (5 +
9 + 2 + 4 + 8 + 2) = 30, which is divisible by 3.
• But, 864329 is not divisible by 3, since sum of its digits
=(8 + 6 + 4 + 3 + 2 + 9) = 32, which is not divisible by 3.

20. Last 3 multiple of 8
• Find the value of K when 425K is divisible by 8..
a) 6
b) 5
c) 0
d) 4

21. Rule of 2 than 9
• A number A4571203B is divisible by 18. Which
of the
• following values can A and B take ?
a) 1, 2
b) 2, 3
c) 6, 8
d) 3, 3

22. Rule of 8 and 11
• Find A and B , if 3765A56682B is divisible by
88?

23. 21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
……
2
4
8
6 4k
Power Cycle

24. 4k = 2, 3, 7, 8
2k = 4, 9
1k = 1, 5, 6, 0
• 1 = 1, 1, 1, …
• 2 = 2, 4, 8, 6…
• 3 = 3, 9, 7, 1…
• 4 = 4, 6, 4, 6
• 5 = 5, 5, 5, 5…
• 6 = 6, 6, 6, 6…
• 7 = 7, 9, 3, 1…
• 8 = 8, 4, 2, 6…
• 9 = 9, 1, 9, 1…
• 0 = 0, 0, 0, 0

25. • What is the last digit of 360
• What is the last digit of 743
• What is the last digit of 940
• What is the last digit of 56120
• What is the last digit of 26670

26. • Find the unit's digit in
• (264)102 + (264)103
a) 0
b) 2
c) 4
d) 20

27. NMAT• Find the unit's digit in
• (263)102 x (265)103
a) 5
b) 2
c) 4
d) 20

28. Remainder Theorem

29. • Rem (X / A) = Rem (Y/A) x Rem (Z/A)
• Where y and z are factors of X

30. • Find the remainder of
a) 24^3 / 7
b) 72^6 / 12
c) 625^12 / 12

31. • Find the remainder when 2^246 is divided by
7.
a) 1
b) 3
c) 7
d) 9
e) none of these

32. 3^2720
• Find the right most non zero digit of (30)2720
• a.1 b.3 c.7 d.9.

33. Euler’s Theorem

35. N + 1 / N is always 1
N – 1 / N is always 1, -1
• Find the remainder when 3560 is divided by 2.
a) 5
b) 2
c) 4
d) 1

36. N + 1 / N is always 1
N – 1 / N is always 1, -1
• Find the remainder when 9560 is divided by 2 =
• 33560 is divided by 2 =
• 5560 is divided by 4 =

37. N – 1 / N is always 1, -1
• Find the remainder when 7560 is divided by 2 =
• 31560 is divided by 2 =
• 3560 is divided by 4 =

38. 16 / 17 = -1
So 2 – 1 = 1
CAT 2002
• Find the remainder when 2256 is divided by 17 =
a) 3
b) 1
c) 7
d) 9.

39. 2.2256
16 / 17 = -1
So 2 – 1 = 1
• Find the remainder when 2257 is divided by 17 =
A. 3
B. 2
C. 7
D. 9

40. Cyclic Remainders

41. 541 / 7 = 5
542 / 7 = 25 / 7 = 4
543 / 7 = 20 / 7 = 6
544 / 7 = 2
545 / 7 = 3
546 / 7 = 1
XAT LEVEL
• Find the remainder when 54120 is divided by 7 =
a) 3
b) 1
c) 7
d) 9.

42. 41 / 6 = 4
42 / 6 = 4
……
CAT 2003
• Find the remainder when 496 is divided by 6 =
a) 3
b) 4
c) 7
d) 9

43. •An+Bn
• Is always divisible by A + B for all
odd n

44. •An - Bn
• Is always divisible by A - B for all odd n
• Is always divisible by A - B for all even n
• Is always divisible by A + B for all even n

45. 351 - 231 = 12
SNAP
• Find the remainder when
• 3523 - 2323 is divided by 12
a) 3
b) 0
c) 7
d) 9

46. 352 - 232 = 12, 58
• Find the remainder when
• 3522 - 2322 is divided by 58
a) 3
b) 0
c) 7
d) 9.

47. 7+6 = 13;
73 – 63 = 127
CAT 2002
• Find the remainder when
• 76n – 66n is divided by ?
a) 13
b) 127
c) 559
d) All of these

48. Highest powers in n!

49. 780/7 + 780/49 + 780/343
CMAT
• Find the highest power of 7 which will divide 780!
a) 13
b) 127
c) 559
d) 15

50. 250/5 + 250/25 + 250/125
• Find the highest power of
• 25 which will divide 250!
a) 13
b) 127
c) 559
d) 31

51. Wilson's Theorem
• Let p be an integer greater than one. p is prime if and only if (p-1)! = -1 (mod p).This
beautiful result is of mostly theoretical value because it is relatively difficult to
calculate (p-1)! In contrast it is easy to calculate ap-1, so elementary primality tests are
built using Fermat's Little Theorem rather than Wilson's. Neither Waring or Wilson
could prove the above theorem, but now it can be found in any elementary number
theory text. To save you some time we present a proof here.
• Proof. It is easy to check the result when p is 2 or 3, so let us assume p > 3. If p is
composite, then its positive divisors are among the integers1, 2, 3, 4, ... , p-1 and it is
clear that gcd((p-1)!,p) > 1, so we can not have (p-1)! = -1 (mod p).
• However if p is prime, then each of the above integers are relatively prime to p. So for
each of these integers a there is another such that ab = 1 (mod p). It is important to
note that this b is unique modulo p, and that since p is prime, a = b if and only if a is 1
or p-1. Now if we omit 1 and p-1, then the others can be grouped into pairs whose
product is one showing2.3.4.....(p-2) = 1 (mod p) (or more simply (p-2)! = 1 (mod p)).
Finally, multiply this equality by p-1 to complete the proof.

52. Vedic Numbers

53. Rem. Of(17/12*19/12*21/12)

54. • Let N=1421*1423*1425.What is the remainder
when N is divided by 12?
a) 0
b) 9
c) 3
d) 6

55. 2^4+2/5=3.
• What is the remainder when (2^100 + 2) is
divided by 101?
a) 3
b) 4
c) 5
d) 6

56. 2^n & 5^n=n+1.
• The values of numbers 2^2004 and 5^2004 are
written one after another. How many digits are
there in all?
a) 4008
b) 2003
c) 2005
d) none of these

57. 3^2720=1.
• Find the right most non zero digit of
(30)^2720.
a) 1
b) 3
c) 7
d) 9.

58. A^n + B^n=divisible by a+b
• The remainder, when (15^23 + 23^23) is divided by
19 is:
a) 4
b) 0
c) 15
d) 18.

59. Divisibility rule of 27
• What is the remainder of 22222222222….(27
times) is divided by 27?
a) 0
b) 1
c) 3
d) 4

60. N^n+1 /n=1
• Find the remainder when 2009^2010 is divided
by 2011.
a) 2010
b) 0
c) 1
d) 2009

61. Understand the format of Q
• 111^111 +222^111 +333^111
+444^111+….999^111 is divided by 555?
a) 1
b) 0
c) 2
d) 3
e) 4

62. 1! +2*2!/3=rem. is 2
• Let N!=1*2*3*4*5*6*N for N greater or equal to 1.
• If P=1! +(2*2!) +(3*3!) +(4*4!)……(12*12!). Find the
remainder when P is divided by 13.
a) 11
b) 1
c) 2
d) 12

63. • If R=30^65 -29^65/30^64+29^64. then,
a) 0<R<1
b) 0.5<R<1
c) 0<0.1
d) R>1

64. 306 is divisible by 3, 6, 9
• 3066 - 306 is not divisible by which of the
following ?
a) 3
b) 4
c) 6
d) 9

65. We need 1 even and two odd
• P,Q& R form a set if distinct prime numbers less
than 20.How many such prime numbers are
possible for which the sum of P,Q & R is even.
a) 15
b) 21
c) 24
d) 28

66. • Q5. (153)8 = (x)10.
a) 162
b) 107
c) 166
d) 207
e) 203

67. Find the last two digits if 1733^148.

68. • Finding the last n second last digit
• (2^10)even= 24
• (2^10)odd =76

69. • Finding the last n second last digit
• For odd digits
• (21)^27= 41
• (31)^21=31
• (a1)^cd = ad1

70. Concept of perfect squares
examining the nature of all perfect
squares…
Any number will have a unit’s digit
as..
1,2,3,4,5,6,7,8,9,0.
Examining the nature of 1.
1^2=01
11^2=121
21^2=441
31^2=961 n so on…
Nature of 2.
2^2=04
12^2=144
22^2=484
32^2=1024 n so on…
Nature of 3.
3^2=09
13^2=169
23^2=529
33^2=1089..
Nature of 4
4^2=16
14^2=196
24^2=576
34^2=1156..
Nature of 5
5^2=25
15^2=225
25^2=625
35^2=1225..
Nature of 6
6^2=36
16^2=256
26^2=576..
Nature of 7
7^2=49
17^2=289
27^2=729..
Nature of 8
8^2=64
18^2=324
28^2=784..
Nature of 9
9^2=81
19^2=361
29^2=841..

71. 74= 2401 => last digit 1
78= 5764801 => last digit
1
72008 = 1 , cyclist of four.
What is the last two digits of 72008
a) 71
b) 51
c) 01
d) 11

72. X can be even or odd & same
for Y.
If x2 - y2 = 1234
Find the number of integral solutions of x,y.
Where x, y < 150.
a) 4
b) 5
c) 0
d) 8

73. To get the last digit as 9,the
only ways are
1&8,2&7,3&6,4&5,9&0
If x2 + y2 = 3479
Find the number of integral solutions of x,y.
Where x, y < 300.
a) 4
b) 5
c) 0
d) 8

74. ASHITA MEPANI
BOSTON UNIVERSITY
MOHIT DESAI
SYRACRUSE UNIVERSITY
FATEMA AURANGABADI
NORTHEASTERN UNIVERSITY
BHAVISHA DAWDA
NEW YORK UNIVERSITY
MAITRI BUCH
UNIVERSITY OF TEXAS DALLAS
RAVI HARIANI
TUSCON, ARIZONA
SANKET WALAWALKAR
KELLY SCHOOL OF BUSINESS
AMEY BHAVSAR
NEW YORK UNIVERSITY
KUSHAL THAKKAR
CARNEGIE MELLON UNIVERSITY
ANUP DESHPANDE
NEW JERSEY, NOMURA
ROHIT ZAWAR
INDIANNA UNIVERSITY
SAGAR SUCHAK
UNIVERSITY OF TEXAS DALLAS
DARSHI SHAH
NEW YORK UNIVERSITY
AAMIR LAKDAWALA
KAISERSLAUTERN UNIVERSITY, GERMANY
320 + scoring
students from GRE
King
ARCHANA RAMAKRISHNAN
UNIVERSITY OF CALIFORNIA
Target 320+ in GRE

75. THANK YOU!