Number series is an important topic in bank exams and it is widely asked under the Quantitative Aptitude section. This topic evaluates a candidate’s logical thinking, numerical ability and problem-solving speed. Understanding the fundamentals and strategies for solving number series questions effectively is essential for success in exams like SBI Clerk, IBPS PO, RBI Assistant and other banking recruitment tests.
Number Series for Bank Exams
A number series is a sequence of numbers arranged in a particular order based on a specific pattern. The task is to find the logic behind the pattern and predict the next number(s), find the missing number(s) or find the wrong number in the series. This type of question tests how well candidates can identify patterns and apply mathematical rules quickly.
Types of Number Series Questions
- Arithmetic Series: In this series, a constant number is added or subtracted to each term to produce the next term. Example: 5, 10, 15, 20, ? (Pattern: Adding 5 each time)
- Geometric Series: Each term in the series is multiplied or divided by a constant number to get the next term. Example: 3, 6, 12, 24, ? (Pattern: Multiplying by 2 each time)
- Square/Cube Series: This involves numbers that are squares or cubes of consecutive integers. Example: 1, 8, 27, 64, ? (Pattern: Cubes of 1, 2, 3, 4)
- Fibonacci Series: Each number is the sum of the two preceding numbers. Example: 0, 1, 1, 2, 3, 5, 8, ? (Pattern: Adding the last two terms)
- Mixed Series: These are complex series where a combination of different operations or alternating patterns is used. Example: 2, 4, 6, 11, 14, 20, ? (Pattern: Alternating addition and multiplication)
- Pattern-Based Series: Series based on a defined rule involving patterns such as alternate operations, skipping numbers, etc. Example: 3, 7, 15, 31, ? (Pattern: Doubling the previous term and subtracting 1)
Number Series Questions for Bank Exams
Directions (1 – 10): In each of these questions a number series is given. In each series only one number is wrong. Find out the wrong number.
Q1. 15,   22,   6,   30,   – 2,    38,   -10
(a) 15
(b) 22
(c) 6
(d) -2
(e) 38
Q2.  18, 5, 9, 9.5, 23, 54.5, 164.5
(a) 54.5
(b) 18
(c) 5
(d) 9
(e) 164.5
Q3. 102, 158, 218, 282, 350, 422, 500
(a) 102
(b) 218
(c) 350
(d) 500
(e) 422
Q4.  72, 52, 42, 30, 20, 12, 6Â
(a) 72
(b) 42
(c) 30
(d) 6
(e) 52
Q5. 125, 164, 284, 484, 764, 1124
(a) 120
(b) 125
(c) 116
(d) 108
(e) 136
Q6. 375, 384, 394, 410, 434, 468, 514
(a) 384
(b) 514
(c) 394
(d) 375
(e) 434
Q7. 248, 250, 279, 295, 420, 456, 799.
(a) 279
(b) 250
(c) 295
(d) 456
(e) 799
Q8. 16,  22,  28,  40,  56,  76,  100
(a) 22
(b) 28
(c) 56
(d) 16
(e) 40
Q9.  6,  8,  18,  57,  232,  1165,  6996
(a) 57
(b) 8
(c) 6996
(d) 1165
(e) 6
Q10.  15,   14,   26,   75,    296,    1485,    8844
(a) 15
(b) 75
(c) 296
(d) 26
(e) 1485
Directions (11 – 20): In each of these questions a number series is given. Find what comes at the place of question (?) mark.
Q11. 11, 13, 17, 25, 41, ?
(a)73
(b)79
(c)82
(d)90
(e)68
Q12. 21, ?, 46, 66, 91, 121
(a)39
(b)31
(c)29
(d)27
(e)33
Q13. 3, 6, 14, 38, ?, 206
(a)154
(b)126
(c)86
(d)112
(e)72
Q14. 2, 12, ?, 240, 720, 1440
(a)72
(b)84
(c)36
(d)60
(e)48
Q15. 3, 6, ?, 42, 123, 366
(a)12
(b)24
(c)15
(d)18
(e)21
Q16. 11, 16.5, 22, 27.5, ?, 38.5
(a)34.5
(b)32
(c)30.5
(d)31.5
(e)33
Q17. 390, 300, 244, 214, ?, 200
(a)210
(b)208
(c)206
(d)204
(e)202
Q18. ?, 45, 36, 43, 34, 41
(a)38
(b)28
(c)36
(d)54
(e)27
Q19. 7, 25, ?, 69, 99, 137
(a)39
(b)58
(c)62
(d)45
(e)57
Q20. 761, 592, 448, 327, ?, 146
(a)302
(b)264
(c)292
(d)276
(e)227
Directions (21-30): What will come in place of question (?) mark in the following number series?
Q21. 25, Â Â 33, Â Â 46, Â Â 69, Â Â 112, Â Â ?
(a) 175
(b) 180
(c) 185
(d) 190
(e) 195
Q22. ? , Â Â 5, Â Â 12, Â Â 39, Â Â 160, Â Â 805
(a) 2
(b) 4
(c) 3
(d) 5
(e) 8
Q23.  11,   24,  41,   62,    ?,   116
(a) 81
(b) 86
(c) 87
(d) 93
(e) 103
Q24. 122,  114,  98,  66,   ?,   -126
(a) 3
(b) 5
(c) 2
(d) 11
(e) 17
Q25.  56,  72,  90,  110,   ?,   156
(a) 132
(b) 90
(c) 73
(d) 93
(e) 87
Q26. 567, 571, ? , 623, 687, 787
(a) 615
(b) 599
(c) 587
(d) 601Â Â
(e) 593
Q27. 167, 118, 76, 42, ?, -4
(a) 17
(b) 14
(c) 18
(d) 16
(e) 25
Q28. ?, 120, 134, 160, 204, 272
(a) 112
(b) 104
(c) 106
(d) 114
(e) 100
Q29. 5, Â Â ? , Â Â 2067, Â Â 2411, Â Â 2537, Â Â 2565 Â
(a) 1337
(b) 1327
(c) 1317
(d) 1307
(e) 1347
Q30. 427, Â Â ? , Â Â 366, Â Â 73.2, Â Â 292.8, Â Â 97.6Â
(a) 51
(b) 41
(c) 61
(d) 71
(e) 31
Directions (31 -45): In each of these questions a number series is given. In each series, only one number is wrong. Find out the wrong number.
Q31. 404, 388, 366, 332, 292, 244, 188
(a) 188
(b) 366
(c) 244
(d) 292
(e) 332
Q32. 512, 255, 127, 63, 31, 15, 7
(a) 15
(b) 31
(c) 127
(d) 512Â Â
(e) 63
Q33. 521, 563, 613, 670, 734, 805, 883
(a) 613
(b) 805
(c) 734
(d) 563
(e) 521
Q34. 137, 149, 179, 235, 325, 457, 630
(a) 630
(b) 149
(c) 325
(d) 457
(e) 179
Q35. 312, 314, 330, 366, 430, 530, 674
(a) 430
(b) 314
(c) 674
(d) 366
(e) 312
Q36. 0.5, 3.5, 21, 105, 420, 1260, 2500
(a) 21
(b) 105
(c) 2500
(d) 420
(e) 3.5
Q37.2249, 2240, 2215, 2166, 2085, 1964, 1796Â
(a) 1796
(b) 2166
(c) 2085
(d) 2240
(e) 1964
Q38. 17, 35, 66, 126, 244, 478, 944
(a) 35
(b) 244
(c) 478
(d) 17
(e) 66
Q39. 114, 154, 202, 258, 322, 394, 478
(a) 394
(b) 478
(c) 202
(d) 322
(e) 258
Q40. 596, 611, 628, 647, 670, 699, 730
(a) 611
(b) 670
(c) 628
(d) 730
(e) 596
Q41. 130, 160, 176,301, 337, 680, 744Â
(a) 130
(b) 337
(c) 301
(d) 160
(e) 176
Q42. 711, 722, 744, 777, 821, 876, 940
(a) 821
(b) 940
(c) 744
(d) 722
(e) 876
Q43. 3, 4, 9, 28, 113, 566, 3396
(a) 113
(b) 566
(c) 3396
(d) 3
(e) 4
Q44. 444, 448, 474, 489, 613, 648, 990
(a) 474
(b) 990
(c) 448
(d) 444
(e) 613
Q45. 125, 343, 81, 1331, 169, 3375, 289
(a) 125
(b) 343
(c) 1331
(d) 289
(e) 81
Tips for Solving Number Series Questions
- Observe Differences: Check the difference between consecutive terms to see if it follows an arithmetic or increasing/decreasing pattern.
- Look for Multiplication or Division: If differences don’t show a pattern, try multiplication or division between terms.
- Check for Squares and Cubes: Identify if the series consists of perfect squares, cubes, or a combination.
- Alternate Patterns: Verify if there are two or more sub-patterns alternating throughout the series.
- Mixed Series: For complex series, consider the possibility of mixed patterns or sequences derived from known series like Fibonacci.
- Practice Time Management: Spend a reasonable amount of time on each question. If a pattern isn’t clear within 30-40 seconds, move on and return later if time permits.
Solutions:
S1. Ans(a)
Sol:
Pattern of series
Wrong number = 15
14+8=22
22-16=6
6+24=30
30 -32= -2
-2+40 =38
38-48 = -10
S2. Ans (a)
Sol. Pattern of series
Wrong number = 54.5
18×0.5-4=5Â
5×1+4=9
9×1.5-4=9.5 Â
9.5×2+4=23 Â
23×2.5-4=53.5
53.5×3+4=164.5 Â
S3. Ans (d)
Sol. Pattern of series
Wrong number = 500
102+56=158
158+60=218
218+64=282Â
282+68=350Â
350+72=422
 422+76=498  Â
S4. Ans (e)
Sol. Pattern of series
Wrong number = 52
8×9=72Â
7×8=56
6×7=42
5×6=30
4×5=20Â
3×4=12
2×3=6
S5. Ans. (b)
Sol. Pattern of series
Wrong number = 125
124+40×1=164Â
164+40×3=284Â
284+40×5=484Â
484+40×7=764Â
764+40×9=1124 Â
S6. Ans.(d)
Sol. Wrong number = 375.
there will be 378 in place of 375.
S7. Ans.(b)
Sol. Wrong number = 250.
there will be 252 in place of 250.
S8. Ans(a)
Sol.
Wrong number = 22
Pattern of series –
 16+4=20
 20+8=28
28+12=40
40+16=56
56+20=76
76+24=100
S9. Ans(e)
Sol.
Wrong number = 6
Pattern of series –
 7×1+1=8
8×2+2=18
 18×3+3=57
 57×4+4=232
 232×5+5=1165
 1165×6+6=6996
S10. Ans (e)
Sol.Â
Wrong number = 1485
Pattern of series –
151-1 = 14
142-2 = 26
263-3 = 75
754-4 = 296
2965-5 = 1475
1475 ×6-6=8844
S11. Ans (a)
Sol.
The pattern of the series–
 11+2=13
 13+4=17
 17+8=25
 25+16=41
 41+32=73
S12. Ans (b)
Sol.
The pattern of the series–
  21+10=31
  31+15=46
  46+20=66
  66+25=91
  91+30=121Â
S13. Ans (c)
Sol.
The pattern of the series–
 3+22-1=6
 6+32-1=14
 14+52-1=38
 38+72-1=86
 86+112-1=206
S14. Ans (d)
Sol.
The pattern of the series–
 2×6=12
 12×5=60
 60×4=240
 240×3=720
 720×2=1440
S15. Ans (c)
Sol.
The pattern of the series–
 3×3-3=6
 6×3-3=15
 15×3-3=42
 42×3-3=123
 123×3-3=366
S16. Ans (e)
Sol.
The pattern of the series–
 11+5.5=16.5
 16.5+5.5=22
 22+5.5=27.5
 27.5+5.5=33
 33+5.5=38.5
S17. Ans (e)
Sol.
The pattern of the series–
 390-10×9=300
 300-8×7=244
 244-6×5=214
 214-4×3=202
 202-2×1=200
S18. Ans (a)
Sol.
The pattern of the series–
 38+7=45
 45-9=36
 36+7=43
 43-9=34
 34+7=41
S19. Ans (d)
Sol.
The pattern of the series–
 7             25               45               69                99              137
            +18             +20             +24                +30             +38
                              +2              +4               +6                +8
S20. Ans (e)
Sol.
The pattern of the series–
 761-132=592
 592-122=448
 448-112=327
 327-102=227
 227-92=146
S21. Ans.(e)
Sol.
S22. Ans.(b)
Sol.
S23. Ans.(c)
Sol.Â
Pattern of series –
S24. Ans.(c)
Sol.Â
Pattern of series –
S25. Ans.(a)
Sol.
Pattern of series –
S26. Ans.(c)
Sol.
S27. Ans.(b)
Sol.
S28. Ans.(a)
Sol.
S29. Ans.(a)
Sol.
Pattern is —
+(11³+1), +(9³+1), +(7³+1), +(5³+1), +(33+1), Â
So, 5 + (11³ + 1) = 1337Â
S30. Ans.(c)
Sol.
Pattern is—
÷7, ×6, ÷5, ×4, ÷3, …
So, 427 ÷ 7 = 61 Â
S31. Ans (b)
Sol.
Pattern of series-Â
 404-16=388
 388-24=364
 364-32=332
 332-40=292
 292-48=244
 244-56=188
So, Wrong number is 366.
S32. Ans (d)
Sol.
Pattern of series-
 511÷2-0.5=255
 255÷2-0.5=127
 127÷2-0.5=63
 63÷2-0.5=31
 31÷2-0.5=15
 15÷2-0.5=7
So, Wrong number is 512.
S33. Ans (e)
Sol.
Pattern of series-Â
520Â Â Â Â Â Â Â 563 Â Â Â Â Â Â Â Â 613 Â Â Â Â Â Â Â 670 Â Â Â Â Â Â Â Â 734 Â Â Â Â Â Â Â Â 805 Â Â Â Â Â 883
         +43       +50         +57        +64        +71        +78
                      +7         +7          +7          +7           +7               Â
So, Wrong number is 521.
S34. Ans (a)
Sol.
Pattern of series-
137+3×4=149
  149+5×6=179
  179+7×8=235
  235+9×10=325
  325+11×12=457
  457+13×14=639
 So, Wrong number is 630.
S35. Ans (e)
Sol.
Pattern of series-
 310+22=314
 314+42=330
 330+62=366
 366+82=430
 430+102=530
 530+122=674
So, Wrong number is 312.
S36. Ans (c)
Pattern of series-
 0.5×7=3.5
 3.5×6=21
 21×5=105
 105×4=420
 420×3=1260
 1260×2=2520
So, Wrong number is 2500.
S37. Ans (a)
Sol.
Pattern of series-
 2249-32=2240
 2240-52=2215
 2215-72=2166
 2166-92=2085
 2085-112=1964
  1964-132=1795
So, Wrong number is 1796.
S38. Ans (d)
Sol.
Pattern of series-
  18.5×2-2=35
 35×2-4=66
 66×2-6=126
 126×2-8=244
 244×2-10=478
 478×2-12=944
So, Wrong number is 17.
S39. Ans (b)
Sol.
Pattern of series-
114 Â Â Â Â Â Â Â 154 Â Â Â Â Â Â Â Â 202 Â Â Â Â Â Â Â Â 258Â Â Â Â Â Â Â Â 322Â Â Â Â Â Â Â Â 394 Â Â Â Â Â Â Â 474Â Â Â Â Â Â Â Â Â Â Â Â Â
           +40        +48         +56         +64         +72        +80           Â
                        +8          +8          +8           +8       +8
So, Wrong number is 478.
S40. Ans. (e)
Sol.
598Â Â Â Â Â Â 611 Â Â Â Â Â Â Â 628 Â Â Â Â Â Â Â 647Â Â Â Â Â Â Â Â 670Â Â Â Â Â Â Â Â 699 Â Â Â Â Â Â 730
         +13       +17        +19        +23        +29       +31   Â
So, Wrong number is 596.
S41. Ans (a)
Sol.
Pattern of series-
 133+33=160
 160+42=176
 176+53=301
 301+62=337
 337+73=680
 680+82=744
So, Wrong number is 130.
S42. Ans (b)
Sol.
Pattern of series-
 711+(11×1)=722
 722+(11×2)=744
 744+(11×3)=777
 777+(11×4)=821
 821+(11×5)=876
 876+(11×6)=942
So, Wrong number is 940.
S43. Ans (c)
Sol.
Pattern of series-
 3×1+1=4
 4×2+1=9
 9×3+1=28
 28×4+1=113
 113×5+1=566
  566×6+1=3397
So, Wrong number is 3396.
S44. Ans (d)
Sol.
Pattern of series-
 445+22-1=448
 448+33-1=474
 474+42-1=489
 489+53-1=613
 613+62-1=648
 648+73-1=990
So, Wrong number is 444.Â
S45. Ans (a)
Sol.
Pattern of series-
 52=25
 73=343
 92=81
 113=1331
 132=169
 153=3375
  172=289
So, Wrong number is 125.
Solutions | |||||||||
01 | a | 02 | a | 03 | d | 04 | e | 05 | b |
06 | d | 07 | b | 08 | a | 09 | e | 10 | e |
11 | a | 12 | b | 13 | c | 14 | d | 15 | c |
16 | e | 17 | e | 18 | a | 19 | d | 20 | e |
21 | e | 22 | b | 23 | c | 24 | c | 25 | a |
26 | c | 27 | b | 28 | a | 29 | a | 30 | c |
31 | b | 32 | d | 33 | e | 34 | a | 35 | e |
36 | c | 37 | a | 38 | d | 39 | b | 40 | e |
41 | a | 42 | b | 43 | c | 44 | d | 45 | a |