**How to Solve Number Series**

**minimum 5 questions of Number Series Questions always ask in most of the Bank , SSC and Other Examinations**. If you know the shortcuts to solve these number series problems then it can be solved easily.

**It takes less time to answer.**Its scoring topics in Quantitative Aptitude. Hence, Its very important to understand shortcuts and some basic ideas to solve these questions quickly.

**ShortCuts#01. Number Series Pattern Based on Whole Number Series:**

**Pattern::01:: Simple Whole Number Series**

Whole Number is: 0,1,2,3,4,5,......

Example: 0, 1, 2, 3, 4, 5, 6, ?

Solution: Since, its a whole number series, so ?=7

**Pattern::02:: Square of Whole Number Series**

Example: 0, 1, 4, 9, 16, 25, 36, ?

Solution: Since, its a square of whole number series, so ?=7*7=49

**Pattern::03:: Cube of Whole Number Series**

Example: 0, 1, 8, 27, ?

Solution: Since, its a cube of whole number series, so ?=4*4*4=64

**Pattern::04:: nth power of Whole Number Series**

Example(Let n=5): 0, 1, 32, ?

Solution: Since, its a 5th power of whole number series, so ?=3*3*3*3*3=243

**ShortCuts#0**

**2. Number Series Pattern Based on Natural Number Series:**

**Pattern::01:: Simple Natural Number Series**

Natural Number is: 1,2,3,4,5,......

Example: 1, 2, 3, 4, 5, 6, ?

Solution: Since, its a natural number series, so ?=7

**Pattern::02:: Square of Natural Number Series**

Example: 1, 4, 9, 16, 25, 36, ?

Solution: Since, its a square of natural number series, so ?=7*7=49

**Pattern::03:: Cube of Natural Number Series**

Example: 1, 8, 27, ?

Solution: Since, its a cube of natural number series, so ?=4*4*4=64

**Pattern::04:: nth power of Natural Number Series**

Example(Let n=5): 1, 32, ?

Solution: Since, its a 5th power of natural number series, so ?=3*3*3*3*3=243

**ShortCuts#0**

**3. Number Series Pattern Based on Even Number Series:**

**Pattern::01:: Simple Even Number Series**

Even Number is: 2, 4, 6, 8, 10, 12, .........

Example: 2, 4, 6, 8, ?

Solution: Since, its an even number series, so ?=10

**Pattern::02:: Square of Even Number Series**

Example: 4, 16, 36, 64, ?

Solution: Since, its a square of even number series, so ?=10*10=100

**Pattern::03:: Cube of Even Number Series**

Example: 8, 64, 216, ?

Solution: Since, its a cube of even number series, so ?=8*8*8=512

**Pattern::04:: nth power of Even Number Series**

Example(Let n=4): 16,256, 1296, ?

Solution: Since, its a 5th power of even number series, so ?=8*8*8*8=4096

**ShortCuts#0**

**4. Number Series Pattern Based on Odd Number Series:**

**Pattern::01:: Simple Odd Number Series**

Odd Number is: 1, 3, 5, 7, 9, 11, ...............

Example: 1, 3, 5, 7, ?

Solution: Since, its an odd number series, so ?=9

**Pattern::02:: Square of Odd Number Series**

Example: 1, 9, 25, 49, 81, ?

Solution: Since, its a square of odd number series, so ?=11*11=121

**Pattern::03:: Cube of Odd Number Series**

Example: 1, 27, 125, ?

Solution: Since, its a cube of odd number series, so ?=7*7*7=343

**Pattern::04:: nth power of Odd Number Series**

Example(Let n=5): 1, 243, 3125, 16807, ?

Solution: Since, its a 5th power of odd number series, so ?=9*9*9*9*9=59049

**ShortCuts#0**

**5. Number Series Pattern Based on Prime Number Series:**

**Pattern::01:: Simple Prime Number Series**

Prime Number is: 2, 3, 5, 7, 11, .............

Example: 2, 3, 5, 7, ?

Solution: Since, its a prime number series, so ?=11

**Pattern::02:: Square of Prime Number Series**

Example: 4, 9, 25, 49, 121, ?

Solution: Since, its a square of prime number series, so ?=13*13=169

**Pattern::03:: Cube of Prime Number Series**

Example: 8, 27, 125, ?

Solution: Since, its a cube of prime number series, so ?=7*7*7=343

**Pattern::04:: nth power of Prime Number Series**

Example(Let n=5): 32, 243, 3125, ?

Solution: Since, its a 5th power of prime number series, so ?=7*7*7*7*7=16807

**ShortCuts#0**

**6. Number Series Pattern Based on Integer:**

**Pattern::01:: Simple Integer**

Integer is: ..............,-4,-3,-2,-1,0,1,2,3,4,....................

Example: -4,?,-2,-1,0,1,2,3

Solution: Since, its a simple integer series, so ?=-3

**Pattern::02:: Square of Integer**

Example: 16,?,4,1,0,1,4,9

Solution: Since, its a square of integer, so ?=-3*-3=9

**Pattern::03:: Cube of Integer**

Example: -64,?,-8,-1,0,1,8,27

Solution: Since, its a cube of integer, so ?=-3*-3*-3=-27

**Pattern::04:: nth power of Integer**

Example(Let n=5): -1024,?,-32,-1,0,1,32,243

Solution: Since, its a 5th power of integer, so ?=-3*-3*-3*-3*-3=-243

**ShortCuts#07**

**. Number Series Based on continuous increasing or decreasing by a specific term :**

**Pattern::01:: C**

**ontinuous Increasing**

Example: 88, 90, 92, 94, ?

Solution: Since, its a continuous increasing series by +2, so ?=94+2=96

**Pattern::01:: C**

**ontinuous Decreasing**

Example: 67, 61, 55, 49, ?

Solution: Since, its a continuous decreasing series by -6, so ?=49-6=43

**ShortCuts#08**

**. Number Series Based on continuous product or division by a specific term :**

**Pattern::01:: C**

**ontinuous Multiplication/Product**

Example: 12.5, 25, 50, 100 200, ?

Solution: Since, its a continuous multiplication series by *2, so ?=200*2=400

**Pattern::01:: C**

**ontinuous Division**

Example: 100, 50, 25, ?

Solution: Since, its a continuous division series by 2, so ?=25/2=12.5

**ShortCuts#09**

**. Number Series Based on *x+y :**

Example: 13, 41, 125, ?

Solution: Since, its pattern is *3+2, so ?=125*3+2=252

[Note: *, +, - and / any two or three or more operations can take place.]

**ShortCuts#09**

**. Number Series Based on Combination of two series:**

Example: 5, 9, 25, 81, 125, 729, 625, ?

Solution: Since, its the combination of two number series which can be observed:

Series 1: 5, 25, 125, 625

Logic: Each term is multiplied by 5 to get next term.

Series 2: 9, 81, 729, ?

Logic: Each term is multiplied by 9 to get next term, so next term = 729*9 = 6561

**ShortCuts#09**

**. Number Series Based on triangular shaped solution :**

Example: 15, 15, 23, 55, 135, ?

Solution:

**Types of Number Series Ask in the Exams:**

**1. Missing Number Series:**

Example: 1, 3, 5, ?, 9, 11

Solution: Since, its an odd number series, so ?=7

**2. Wrong Number Series:**

Example: 2, 4, 6, 8, 13, 12

Solution: From the given series it can be observed that it should be an even number series, 13 is placed a wrong number, in place of 13, there should be 10.

**3. Next Term Number Series:**

Example: 2, 3, 5, 7, ___

Since, Its a prime number series, so next term will be 11.

**4. New type of Number Series generally ask in Bank PO Examination:**

Example:

3 19 103 439 1381 2887

5 (a) (b) (c) (d) (e)

What will come in place of (b) ?

Solution: The given series is based on the following pattern : ×6+1,×5+8,×4+27,×3+64,×2+125

Similarly, 5×6+1=31

31×5+8=163

Hence, 163 will come in place of (b).

**Solve These Important Number Series Questions asked in Various Competitive Examinations:**

**Directions (Q1-Q19) : What should come in place of question-mark (?) in the following number series ?**

Q1. 8, 7, 13, 38, 151, ?

Q2. 9, 5, 6, 10.5, 23, ?

Q3. 18, 20, 26, 38, ?, 88

Q4. 1, 20, 58, 134, ?, 590

Q5. 2, ?, 256, 1024, 2048, 2048

Q6. 190, 94, 46, 22 ?

Q7. 7, 4, 5, 12, 52, ?

Q8. 6, 4, 5, 11, 39, ?

Q9. 89, 88, 85, 78, 63, ?

Q10. 5, 28, 47, 64, 77, ?

Q11. 7, 3, 2, 2, 4, ?

Q12. 2, 13, 26, 43, 62, ?

Q13. 519, 517, 509, 483, 403, ?

Q14. 27, 38, 51, 68, 87, ?

Q15. 2, 8, 28, 54, 53, ?

Q16. 167, 164, 159, 150, ? , 100

Q17. 17, 31, 15, 33, 13 , ?

Q18. 973, 325 , 109 , 37 , 13 , ?

Q19. 0.5 , 2, 8, 35, ? , 1079

**Directions (Q20-Q24): In the following number series, a wrong number is given. Find out that wrong number.**

Q20. 2 11 38 197 1172 8227 65806

(a) 11

(b) 38

(c) 197

(d) 1172

(e) 8227

Q21. 16 19 21 30 46 71 107

(a) 19

(b) 21

(c) 30

(d) 46

(e) 71

Q22. 7 9 16 25 41 68 107 173

(a) 107

(b) 16

(c) 41

(d) 68

(e) 25

Q23. 4 2 3.5 7.5 26.25 118.125

(a) 118.125

(b) 26.25

(c) 3.5

(d) 2

(e) 7.5

Q24. 16 4 2 1.5 1.75 1.875

(a) 1.875

(b) 1.75

(c) 1.5

(d) 2

(e) 4

**Directions (Q25-Q29) : In each of the following questions a number series is given. After the series a number is given followed by (a), (b), (c), (d) and (e). You have to complete the series starting with the given number, following the sequence of original series and answer the questions that follow the series.**

Q25. 3 19 103 439 1381 2887

5 (a) (b) (c) (d) (e)

What will come in place of (b) ?

(a) 139

(b) 163

(c) 161

(d) 157

(e) None of these

Q26. 4 13 40 135 552 2765

2 (a) (b) (c) (d) (e)

What will come in place of (c) ?

(a) 123

(b) 133

(c) 127

(d) 131

(e) None of these

Q27. 5 12 4 10 3 8

6 (a) (b) (c) (d) (e)

What will come in place of (d) ?

(a) 3

(b) 5

(c) 4

(d) 7

(e) None of these

Q28. 3 13 37 87 191 401

1 (a) (b) (c) (d) (e)

What will come in place of (d) ?

(a) 169

(b) 161

(c) 171

(d) 159

(e) None of these

Q29. 8 4 6 15 52.5 236.25

12 (a) (b) (c) (d) (e)

What will come in place of (c) ?

(a) 23.5

(b) 16.5

(c) 22.5

(d) 22.25

(e) None of these

**Directions (Q30-Q34) : What should come in place of question-mark (?) in the following number series ?**

Q30. 13 14 30 93 376 1885 ?

(a) 10818

(b) 10316

(c) 11316

(d) 11318

(e) None of these

Q31. 4 6 9 13.5 20.25 30.375 ?

(a) 40.25

(b) 45.5625

(c) 42.7525

(d) 48.5625

(e) None of these

Q32. 400 240 144 86.4 51.84 31.104 ?

(a) 19.2466

(b) 17.2244

(c) 16.8824

(d) 18.6624

(e) None of these

Q33. 9 4.5 4.5 6.75 13.5 33.75 ?

(a) 101.25

(b) 103.75

(c) 99.75

(d) 105.50

(e) None of these

Q34. 705 728 774 843 935 1050 ?

(a) 1190

(b) 1180

(c) 1185

(d) 1187

(e) None of these

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