helpful for aspirants of various exams

1. VERBAL REASONING
NUMBER SERIES

2. Number series
• A SERIES IS GIVEN AND WE
HAVE TO FIND THE NEXT TERM
OF THE SERIESOF THE SERIES
• THE TERMS FOLLOW A FIXED
PATTERN
• WE NEED TO DETECT THAT
PATTERN

3. •TECHNIQUE TO
SOLVE THE
NUMBER SERIESNUMBER SERIES

4. • TRY TO FIND THE PATTERN OF
THE SMALLER NUMBERS
BECAUSE THEY HAVE LESS
MAGNITUDE
• SEARCH FOR THE PATTERN
FROM THE 1,2,3,4 TERMS OF
THE SERIES IE THINK ON THE
START OF THE SERIES

5. 1, 7 , 13, 19 ,25 ?

6. •VARIOUS TYPES OF SERIES
•TYPES OF LOGIC USED TO
IDENTIFY THE VARIOUS
TYPES OF PATTERNS OFTYPES OF PATTERNS OF
THE NUMBERS OF THE
SERIES

7. TYPE -1 --------
PATTERNS BASED
ON TYPE OFON TYPE OF
NUMBERS IN THE
SERIES

8. • 1] PRIME NUMBERS
• 2] ODD NUMBERS
• 3]EVEN NUMBERS
• 4] ODD EVEN MIXED
• 5] ODD EVEN PRIME NUMBERS MIXED• 5] ODD EVEN PRIME NUMBERS MIXED
• 6] SQUARE NUMBERS
• 7] CUBE NUMBERS
• 8] NUMBERS BASED ON DIVISIBILITY LIKE
DIVISIBLE BY
2,3,4,5,6,7,8,9,11,13,17,19,23

9. • EXAMPLES
• 2,4,16,216------------------
• 1,3,5,7,9----------------
• 2,3,5,7,11,13,17,19,23------------2,3,5,7,11,13,17,19,23------------
• 2,4,3,16,5,216,7---------------
• 2,8,512-------------------
• 11,44,55,66,77,--------------

10. •TYPE -2 ----PATTERNS
BASED ON SOME
MATHEMATICAL
OPERATIONSOPERATIONS
PERFORMED ON THE
TERMS OF SERIES

11. • LET THE TERM OF THE SERIES BE
X
• SO WE WILL DENOTE THE TERM
OF THE SERIES BY X
• NOW ALL THE PATTERNS WILL• NOW ALL THE PATTERNS WILL
INVOLVE X TO GET
UNDERSTANDING OF VARIOUS
TYPES OF PATTERNS USED IN THE
NUMBER SERIES

12. • 1] ADDITION BASED
• X -------------- X + FIXED NUMBER
• 3,8------------------SERIES
• 3------------ ---3 + 5
• 2] SUBSTRACTION BASED
• X ---------------- X – FIXED NUMBER
• 28,25----------------SERIES
• 28-----------------------28 - 3

13. •3] PRODUCT BASED
•X -------------------X * FIXED
NUMBER
•25,150---------------------•25,150---------------------
SERIES
•25-------------------25*6 -------

14. • 4] division based
• X-----------------X/ FIXED NUMBER
• 152,8------------------------SERIES• 152,8------------------------SERIES
• 152-----------------------152/19

15. 5] COMBINATION OF ALL
BASIC MATHEMATICAL
OPERATIONS ON TERM
OF THE SERIESOF THE SERIES
related to fixed same
number

16. • X--------------(X + NUMBER)/NUMBER
• X--------------(X - NUMBER)/NUMBER
• X---------------(X * NUMBER) + or -
NUMBER
• X---------------(X / NUMBER ) +• X---------------(X / NUMBER ) +
NUMBER
• X---------------(X/NUMBER ) -
NUMBER

17. • EXAMPLES
• 5,12 -----------------5X2 + 2 = 12
• 6,15-----------------6x3 - 3 = 15
• 30,11----------------30/6 + 6 = 1130,11----------------30/6 + 6 = 11
• 12,5 ------------------(12+ 3)/3 = 5
• 16,7------------------(16 -2) /2 = 7

18. 6] WHEN THE MATHEMATICAL
OPERATIONS ARE PERFORMED BUT
TWO NUMBERS ARE USED IE X IS
RELATED TO 2 different numbers
NUMBER 1 AND NUMBER 2
EG --------------
X ----------------- X/NUMBER1 (+/-)X ----------------- X/NUMBER1 (+/-)
NUMBER 2
X------------------X(+/-) NUMBER1 (/)
NUMBER 2

19. • EXAMPLES -----------
• 12,64 -------------------12*5 + 4 =
64
• 11,60 -------------------11*6 - 6 =
6060
• 95,16-------------------95/5 - 3 =
16
• 68,10------------------68/17 + 6 = 10

20. • 7] when then term of series is
mathematically related to a number
with a particular property like a prime
number , or square of number or a cube
of number
• Eg ----- X -------------X + PRIME NUMBER
• 15, 29 -------------------15 + 11
• 15, 40 ------------------15 + SQUARE OF 5
• 15, 6 --------------------15 - SQUARE OF 3

21. • TYPE -3 –WHEN THE SAME TERM OF THE SERIES
IS USED IN THE PATTERN
• EG ------X---------------X + (CUBE OF X)
• X---------------X - (SQUARE OF X)
• X---------------X + ( X/ Number )
• X---------------X - ( X/ Number)• X---------------X - ( X/ Number)
• X ---------------SQUARE ROOT OF X
• X ---------------CUBE ROOT OF X
• X--------------- X – (SQUARE ROOT OR CUBE
ROOT OF X)

22. • Type -4 --- When different number is
used to show the term
• Eg --------- X = ( number ) + (
number )
• Eg -----------X =( number ) + ( square
or cube of number)
• Eg -----------X = (NUMBER ) – (• Eg -----------X = (NUMBER ) – (
number)
• Eg -----------X = ( number ) – (square
or cube of number)

23. • Note -----
• X = number 1 (+/-) number 2
• X = square of number 1 (+/-)
square of number 2
• Similarly for cube, square root etc
• NUMBER 1 IS NOT EQUAL TO
NUMBER 2

24. •Combination of 2 series
•---ABCD DENOTE
NUMBERS
•A B C D E F G H I J

25. Solved examples
• Ex. 1. Which is the number that
comes next in the sequence :
0. 6. 24. 60. 120. 210 ?
Cube of 1 – 1 , cube of 2 – 2 -----Cube of 1 – 1 , cube of 2 – 2 -----
• Ans = 336 -----------cube of 7 – 7

26. • Ex. 3. Which is the number that comes next in
the following sequence ?
4, 6, 12, 14,28, 30, ( )
• a) 32 b) 60 c) 62 d) 64
4, 6. 12, 14. 28, 30. ( )SOLN ------4, 6. 12, 14. 28, 30. ( )
B
Pattern in both series = +8, +16, +32

27. Q] 1,2, 6,24, ( )
PATTERN = X 2 , X 3 ,X 4, X 5
ANS = 24 X 5 = 120
Q] 3, 12, 27, 48, 75, 108, ( )Q] 3, 12, 27, 48, 75, 108, ( )
PATTERN = 3x square of 1
= 3x square of 2
= 3x square of 3
Ans = 147

28. Q] 3. 7, 15, 31. 63. ( )
Thus. (3 x 2) + 1 = 7, (7x2) + 1 =
15,
(15x2)+l = 31 and so on.(15x2)+l = 31 and so on.
Missing number =(63 x 2) + 1 =
127.

29. Q] 66. 36, 18. ( )
Each number in the series is the
product of the digits of the
preceding number.
Thus, 6 x 6 a 36. 3 x 6 « 18 and soThus, 6 x 6 a 36. 3 x 6 « 18 and so
on.
Missing number =1x8 = 8(ANS)

30. Q] 2, 3, 8, 63, ( )
Each term in the series is one less than the
square of the preceding term.
Thus.
2(SQUARE) - 1 = 3,
3(SQUARE) - 1 = 8,3(SQUARE) - 1 = 8,
8(SQUARE) - 1 = 63.
ANS = 63(SQUARE) – 1