Quantitative Aptitude - SPLessons

Number Series Practice Sets

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Number Series Practice Sets

shape Introduction

Number Series is one of the important topic in the Quantitative Aptitude section . Number Series is the arrangement of numbers in a certain order where some numbers are wrongly kept or some numbers are missing from that series. So accurate series are to be found. Number Series in competitive exams are divided into two. One is missing series and the other is wrong series. A number series is given in which a number is wrongly placed is the wrong series. Candidates are asked to identify that particular wrong number. A number series in which a specific number is missing is the missing series. Candidates have to identify the missing number. The article Number Series Practice Sets lists important number series practice questions for competitive exams like RRB ALP/Technical Exams/Junior Engineer Recruitment Exams, SSC, IBPS PO Exams and etc.


shape Quiz

Direction: In the following number series, a wrong number is given. Find out that wrong number.


1. 2 11 38 197 1172 8227 65806

    A. 11
    B. 38
    C. 197
    D. 1172
    E.2


2. 3601 3602 1803 604 154 36 12

    A. 3602
    B. 1803
    C. 604
    D. 154
    E. 365


3. 7.25 47.5 87.5 157.5 247.5 357.5 487.5

    A. 37.5
    B. 87.5
    C. 157.5
    D. 7.5
    E. 365


4. 1 2 4 9 23 69 186

    A. 2
    B. 9
    C. 23
    D. 4
    E. 69


5. 1 3 10 36 152 760 4632

    A. 3
    B. 36
    C. 4632
    D. 760
    E. 152


Direction: In the following number series, a wrong number is given. Find out that wrong number.


6. 1 4 25 256 3125 46656 823543

    A. 4
    B. 823543
    C. 46656
    D. 25
    E. 256


7. 1 513 31 61125 253

    A. 1
    B. 5
    C. 31
    D. 61
    E. 125


8. 119 130 129 154 203 284 405

    A. 130
    B. 129
    C. 154
    D. 203
    E. 405


9. 150 290 560 1120 2140 4230 8400

    A. 2140
    B. 560
    C. 1120
    D. 4230
    E. 290


10. 157.5 45 15 6 3 2 1

    A. 1
    B. 2
    C. 6
    D. 157.5
    E. 45


Answers and Explanation

1. Answer Option D

Explanation – The series is based on the following pattern:

11= 2 × 3 + 5

38= 11 × 4 – 6

197 = 38 × 5 + 7

1172 197 × 6 – 8

1172 is wrong and it should be replaced by 197 × 6 – 8 = 1174


2. Answer Option D

Explanation – The sequence is based on following pattern:

\(\frac{3601}{1}\) + 1 = 3602

\(\frac{3602}{2}\) + 1 = 1801 + 2 = 1803

\(\frac{1803}{3}\) + 3 = 601 + 3 = 604

\(\frac{604}{4}\) + 4 = 151 + 4 = 155 \(\neq\) [154]

\(\frac{155}{5}\) + 5 = 31 + 5 = 36

\(\frac{36}{6}\) + 6 = 6 + 6 = 12


3. Answer Option A

Explanation – The series is based on the following pattern:

487.5 – 357.5 = 130

357.5 – 247.5 = 110

247.5 – 157.5 = 90

157.5 – 87.5 = 70

87.5 – 47.5 = \(\neq\) [40]

87.5 – 37.5 = 50

37.5 – 7.5 = 30

Clearly, 47.5 is the wrong number. It should be replaced by 37.5.


4. Answer Option E

Explanation –The pattern is :

1 × 3 – 1 = 2

2 × 3 – 2 = 4

4 × 3 – 3 = 9

9 × 3 – 4 = 23

23 × 3 – 5 = 69 – 5 = 64 \(\neq\) [69]

64 × 3 – 6 = 192 – 6 = 186


5. Answer Option D

Explanation – The pattern is :

1 × 1 + 2 = 3

3 × 2 + 4 = 10

10 × 3 + 6 = 36

36 × 4 + 8 = 152

152 × 5 +10 = 770 \(\neq\) [760]

770 × 6 + 12 = 4632


6. Answer – Option D

Explanation –

The pattern of the number series is:


\({1}^{1}\) = 1


\({2}^{2}\) = 4


\({3}^{3}\) = 27 \(\neq\) [25]


\({4}^{4}\) = 256


\({5}^{5}\) = 3125


\({6}^{6}\) = 46656


7. Answer – Option C

Explanation –

The pattern of the number series is:


1 + \({2}^{2}\) = 1 + 4 = 5


5 + \({2}^{3}\) = 5 + 8 = 13


13 + \({2}^{4}\) = 13 + 16 = 29 \(\neq\) [31]


29 + \({2}^{5}\) = 29 + 32 = 61


61 + \({2}^{6}\) = 61 + 64 = 125


8. Answer – Option A

Explanation –

The pattern is :


119 + \({1}^{2}\) = 119 + 1 = 120 \(\neq\) [130]


120 + \({3}^{2}\) = 120 + 9 = 129


129 + \({5}^{2}\) = 129 + 25 = 154


154 + \({7}^{2}\) = 154 + 49 = 203


203 + \({9}^{2}\) = 203 + 81 = 284


284 + \({11}^{2}\) = 284 + 121 = 405


9. Answer – Option C

Explanation –

The pattern is:


150 × 2 – 1 × 10


= 300 – 10 = 290


290 × 2 – 2 × 10


= 580 – 20 = 560


560 × 2 – 3 × 10 = 1120 – 30


= 1090 \(\neq\) [1120]


1090 × 2 – 4 × 10


= 2180 – 40 = 2140


2140 × 2 – 5 × 10


4280 – 50 = 4230


10. Answer – Option A

Explanation –

The pattern is :


\(\frac{157.5}{3.5}\) = 45


\(\frac{45}{3}\) = 15


\(\frac{15}{2.5}\) = 6


\(\frac{6}{2}\)= 3


\(\frac{3}{1.5}\) = 2


\(\frac{2}{1}\) = 2 \(\neq\)[1]

Direction: In the following number series, a wrong number is given. Find out that wrong number.


1. 19 68 102 129 145 154

    A. 154
    B. 129
    C. 145
    D. 102
    E. None of these


2. 2 6 15 30 45 43.5 22.5

    A. 6
    B. 30
    C. 45
    D. 15
    E. 43.5


3. 20 10 12 15 30 75 225

    A. 30
    B. 15
    C. 12
    D. 75
    E. 225


4. 29 37 21 43 13 53 5

    A. 37
    B. 53
    C. 13
    D. 21
    E. 43


5. 3 4 12 45 198 1005 6066

    A. 4
    B. 6066
    C. 45
    D. 1005
    E. 198


Direction: In the following number series, a wrong number is given. Find out that wrong number.


6. 3 5 13 43 176 891 5353

    A. 5
    B. 13
    C. 43
    D. 176
    E. 891


7. 39 43 51 60 87 110 167

    A. 167
    B. 87
    C. 60
    D. 110
    E. 43


8. 4 5 13 40 105 229 445

    A. 4
    B. 13
    C. 105
    D. 445
    E. 229


9. 48 72 108 162 243 366

    A. 72
    B. 108
    C. 162
    D. 243
    E. None of these


10. 5531 5506 5425 5304 5135 4910 4621

    A. 5531
    B. 5425
    C. 4621
    D. 5135
    E. 5506


Answers and Explanations


1. Answer – Option D

Explanation –

19 + \({7}^{2}\) = 19 + 49 = 66


68 + \({6}^{2}\) = 68 + 36 = 104 \(\neq\) [102]


104 + \({5}^{2}\) = 104 + 25 = 129


129 + \({4}^{2}\) = 129 + 16 = 145


145 + \({3}^{2}\) = 145 + 9 = 154


2. Answer – Option E

Explanation –

The pattern of the number series is :


2 × 3 = 6


6 × 2.5 = 15


15 × 2 = 30


30 × 1.5 = 45


45 × 1 = 45 \(\neq\) [43.5]


45 × 0.5 = 22.5


3. Answer – Option C

Explanation –

The pattern is :


20 × 0.5 = 10


10 × 1 = 10 \(\neq\) [20]


10 × 1.5 = 15


15 × 2 = 30


30 × 2.5 = 75


75 × 3 = 225


4. Answer – Option E

Explanation –

The pattern is:


29 + 1 × 8 = 27


37 – 2 × 8 = 37 – 16 = 21


21 + 3 × 8 = 21 + 24 =45 \(\neq\) [43]


45 – 4 × 8 = 45 – 32 = 13


13 + 5 × 8 = 13 + 40 = 53


53 – 6 × 8 = 53 – 48 = 5


5. Answer – Option C

Explanation –

The pattern is :


4 + \({1}^{3}\) = 5


5 + \({2}^{3}\) = 13


13 + \({3}^{3}\) = 40


40 + \({4}^{3}\) = 104 \(\neq\) [105]


104 + \({5}^{3}\) = 229


229 + \({6}^{3}\) = 445


6. Answer – Option C

Explanation –

The pattern of the number of series is:


3 × 1 + 2 = 5


5 × 2 + 3 = 13


13 × 3 + 4 = 43


43 × 4 + 5 = 177 \(\neq\) [176]


177 × 5 + 6 = 891


7. Answer – Option D

Explanation –

The pattern is :


39 + \({2}^{2}\) = 39 + 4 = 43


43 + \({2}^{3}\) = 43 + 8 = 51


51 + \({3}^{2}\) = 51 + 9 = 60


60 + \({3}^{3}\) = 60 + 9 = 69


87 + \({4}^{2}\) = 87 + 16 = 103 \(\neq\) [110]


103 + \({4}^{3}\) = 103 + 64 = 167


8. Answer – Option E

Explanation –

The pattern is :


3 × 1 + \({1}^{2}\) = 3 + 1 = 4


4 × 2 + \({2}^{2}\) = 8 + 4 = 12


12 × 3 + \({3}^{2}\) = 36 + 9 = 45


45 × 4 + \({4}^{2}\) = 180 + 16 = 196 \(\neq\) [198]


196 × 5 + \({5}^{2}\) = 980 + 25 = 1005


1005 × 6 + \({6}^{2}\) = 6030 + 36 = 6066


9. Answer – Option

Explanation –

48 (\(\frac{3}{2}\)) = 72; 72 × (\(\frac{3}{2}\))= 108


108 (\(\frac{3}{2}\)) = 162; 162 (\(\frac{3}{2}\)) = 243


243 (\(\frac{3}{2}\)) = 364.5 \(\neq\) 366


10. Answer – Option

Explanation –

The pattern is :


5531 – 5506 = 25 = \({5}^{2}\)


5555 – 5506 = 49 = \({7}^{2}\)


5506 – 5425 = 81 = \({9}^{2}\)


5425 – 5304 = 121 = \({11}^{2}\)


5304 – 5135 = 169 = \({13}^{2}\)


5135 – 4910 = 225 = \({15}^{2}\)


4910 – 4621 = 289 = \({17}^{2}\)


Clearly, 5531 is wrong, which should be substituted by 5555.

Direction: In the following number series, a wrong number is given. Find out that wrong number.
1. 6 7 16 41 90 154 292

    A. 7
    B. 16
    C. 41
    D. 90
    E. 154


2. 6.5 11.8 22.4 38.3 59.5 87.3 117.8

    A. 22.4
    B. 59.5
    C. 11.6
    D. 38.3
    E. 87.3


3. 66 91 120 153 190 233 276

    A. 120
    B. 233
    C. 153
    D. 276
    E. 190


4. 8 11 17 47 128 371 1100

    A. 11
    B. 47
    C. 17
    D. 371
    E. 128


5. 8 12 24, 46 72 108 152

    A. 12
    B. 24
    C. 46
    D. 72
    E. None of these


Direction: In the following number series, a wrong number is given. Find out that wrong number.


6. 8 276 4125 218 343

    A. 27
    B. 218
    C. 125
    D. 343
    E. None of these


7. 80 42 24 13.5 8.75 6.375 5.1875

    A. 8.75
    B. 13.5
    C. 24
    D. 6.375
    E. 42


8. 850 843 829 808 788 745 703

    A. 843
    B. 829
    C. 808
    D. 788
    E. 745


9. 1331 2197 3375 4914 6859 9261 12167

    A. 4914
    B. 6859
    C. 9261
    D. 2197
    E. 12167


10. 1500 1581 1664 1749 1833 1925 2016

    A. 1581
    B. 1664
    C. 1833
    D. 1925
    E. 1749


Answers and Explanations


1. Answer – Option E

Explanation –

The pattern of the number of series is:


6 + \({1}^{2}\) = 6 + 1 = 7


7 + \({3}^{2}\) = 7 + 9 = 16


16 \({5}^{2}\) = 16 + 25 = 41


41 + \({7}^{2}\) = 41 + 49 = 90


90 + \({9}^{2}\) = 90 + 81 = 171 \(\neq\) [154]


171 + \({11}^{2}\) = 171 + 121 = 292


2. Answer – Option

Explanation –

The pattern is :


6.5 + 5.3 = 11.8


11.8 + 2 × 5.3 = 11.8 + 10.6 = 22.4


22.4 + 3 × 5.3 = 22.4 + 15.9 = 38.3


38.3 + 4 × 5.3 = 38.3 + 21.2 = 59.5


59.5 + 5 × 5.3 = 59.5 + 26.5 = 86 \(\neq\) [87.3]


86 + 6 × 5.3 = 86 + 31.8 = 117 .8


3. Answer – Option

Explanation –

The series is based on the following pattern:


66 + 25 = 91


91 + 29 = 120


120 + 33 = 153


153 + 37 = 190


190 + 41 = 231 \(\neq\) [233]


231 + 45 = 276


Clearly, 233 is wrong number. It should be 231.


4. Answer – Option C

Explanation –

The pattern of the number series is:


8 + \({3}^{1}\) = 11


11 + \({3}^{2}\) = 11 + 9 = 20 \(\neq\) [17]


20 + \({3}^{3}\) = 20 + 27 = 47


47 + \({3}^{4}\) = 47 + 81 = 128


128 + \({3}^{5}\) =128 + 243 = 371


5. Answer – Option C

Explanation –

The pattern is:

8 + 4 × 1 = 12


12 + 4 × 3 = 24


24 + 4 × 5 = 44 \(\neq\) [46]


44 + 4 × 7 = 72


72 + 4 × 9 = 108


6. Answer – Option B

Explanation –

\({2}^{3}\) = 8 : \({3}^{3}\) = 27


\({4}^{3}\) = 64 : \({5}^{3}\) = 125


\({6}^{3}\) = 216 \(\neq\) [218]


\({7}^{3}\) = 343


7. Answer – Option C

Explanation –

The pattern is:


(\(\frac{80}{2}\)) +2 = 40 + 2 = 42


(\(\frac{42}{2}\) ) + 2 = 21 + 2 = 23 \(\neq\) [24]


(\(\frac{23}{2}\) ) + 2 = 11.5 + 2= 13.5


(\(\frac{13.5}{2}\)) + 2 = 6.75 + 2 = 8.75


(\(\frac{8.75}{2}\)) + 2 = 4.375 + 2 = 6.375


8. Answer – Option D

Explanation –

The pattern of the number series is:


850 – 1 × 7 = 843


843 – 2 × 7 = 829


829 – 3 × 7 = 808


808 – 4 × 7 = 780 \(\neq\) [788]


780 – 5 × 7 = 745


745 – 6 × 7 = 703


9. Answer – Option A

Explanation –

The series is based on the following pattern:


11 × 11 × 11 = 1331


13 × 13 × 13 = 2197


15 ×15 × 15 = 3375


17 × 17 × 17 = 4913 \(\neq\) [4914]


19 × 19 × 19 = 6859


Clearly, 4914 is wrong number. It should be replaced by 4913.


10. Answer – Option C

Explanation –

The series is based on the following pattern:


1500 + 81 = 1581


1581 + 83 = 1583


1664 + 85 = 1749


1749 + 87 = 1836 \(\neq\) [1833]


1836 + 89 = 1925


1925 + 91 = 2016


Clearly, 1833 is wrong number. It should be replaced by 1836.

Direction: In the following number series, a wrong number is given. Find out that wrong number.


1. 160 80 120 180 1050 4725 25987.5

    A. 60
    B. 90
    C. 3564
    D. 87.5
    E. 135


2. 2 10 18 54 162 486 1458

    A. 18
    B. 54
    C. 162
    D. 10
    E. None of these


3. 214 18 162 62 143 90 106

    A. -34
    B. 110
    C. 10
    D. 91
    E. 38


4. 250 239 216 181 136 75 4

    A. 239
    B. 181
    C. 75
    D. 216
    E. 136


5. 3 4 10 34 136 685 4116

    A. 22
    B. 276
    C. 72
    D. 374
    E. 12


Direction: In the following number series, a wrong number is given. Find out that wrong number.


6. 3 5 12 38 154 914 4634

    A. 1632
    B. 1222
    C. 1834
    D. 3312
    E. 1488


7. 4 2.5 3.5 6.5 15.5 41.25 126.75

    A. 2.5
    B. 3.5
    C. 6.5
    D. 15.5
    E. 41.25


8. 4 6 18 49 201 1011

    A. 1011
    B. 201
    C. 18
    D. 49
    E. None of these


9. 484 240 120 57 26.5 11.25 3.625

    A. 240
    B. 120
    C. 57
    D. 26.5
    E. None of these


10. 5 348 564 689 716 780 788

    A. 716
    B. 788
    C. 348
    D. 689
    E. 780


Answers and Explanations


1. Answer – Option E

Explanation –

The series is based on following pattern:


160 × 0.5 = 80


80 × 1.5 = 120


120 × 2.5 = [300]


300 × 3.5 = 1050


1050 × 4.5 = 4725


4725 × 5.5 = 25947.5


Therefore, the number 180 is wrong.


i.e, According to the question, the new series starts from the number 180 in the same pattern:


180 × 0.5 = 90


90 × 1.5 = [135]


Hence, the number 135 is required answer.


2. Answer – Option D

Explanation –

The pattern is:


2 × 3 = 6 \(\neq\) [10]


6 × 3 = 18


18 × 3 = 54


54 × 3 = 162


3. Answer – Option D

Explanation –

The series is based on following pattern:


214 – \({(14)}^{2}\) = 18


18 + \({(12)}^{2}\) = 162


162 – \({(10)}^{2}\) = 62


62 + \({(8)}^{2}\) = [126]


126 – \({(6)}^{2}\) = 90


90 + \({(4)}^{2}\) = 106


Therefore, the number 143 is wrong.


i.e, According to the question, the new series starts from the 143 in the same pattern.


143 – \({(14)}^{2}\) = – 53


– 53 + \({(12)}^{2}\) = [91]


Hence, the number 91 is required answer.


4. Answer – Option E

Explanation –

The pattern is :


250 – 11 = 239


239 – (11× 2 + 1) = 239 – 23 = 216


216 – (11 × 3 + 2) = 216 – 35 = 181


181 – (11 × 4 + 3) = 181 – 47 = 134 \(\neq\) [136]


134 – (11 × 5 + 4) = 134 – 59 = 75


75 – (11 × 6 + 5) = 75 – 71 = 4


5. Answer – Option C

Explanation –

The series is based on following pattern:


3 × 1 + 1 = 4


4 × 2 + 2 = 10


10 × 3 + 3 = [33]


33 × 4 + 4 = 136


136 × 5 + 5 = 685


685 × 6 + 6 = 4116


Therefore, the number 34 is wrong.


i.e, According to question, the new series starts from numbers 34 in the same pattern


34 × 1 + 1 = 35


35 × 2 + 2 = [72]


Hence, the number 72 is required answer.


6. Answer – Option C

Explanation –

The series is based on following pattern:


3 × 1 + 2 = 5


5 × 2 + 2 = 12


13 × 3 + 2 = 38


38 × 4 + 2 = 154


154 × 5 + 2 = [772]


772 × 6 + 2 = 4634


Therefore, the number 914 is wrong.


i.e, According to question, the new series is as follows:


914 × 1 + 2 = 916


916 × 2 + 2 = [1834]


1834 × 3 + 2 = 5504


Therefore the required number is 1834


7. Answer – Option C

Explanation –

The pattern of the number series is:


4 × 0.5 + 0.5 = 2 + 0.5 = 2.5


2.5 × 1 + 1 = 3.5


3.5 × 1.5 + 1.5 = 6.75 \(\neq\)[6.5]


6.75 × 2 + 2 = 15.5


15.5 × 2.5 + 2.5 =38.75 + 2.5 = 41.25


41.25 × 3 + 3 = 123.75 + 3 = 126.75


8. Answer – Option C

Explanation –

4 × 1 + 2 = 4 + 2 = 6


4 × 2 + 3 = 12 + 3 = 15 \(\neq\) 18


15 × 3 + 4 = 45 + 4 = 49


49 × 4 + 5 = 196 + 5 = 201


201 × 5 + 6 = 1005 + 6 = 1011


9. Answer – Option B

Explanation –

The pattern of the number series is:


(\(\frac{484}{2}\)) – 2 = 242 – 2 = 240


(\(\frac{440}{2}\)) – 2 = 120 – 2 = 118 \(\neq\) [120]


(\(\frac{118}{2}\)) – 2 = 59 – 2 = 57


(\(\frac{57}{2}\)) -2 = 28.5 – 2 = 26.5


10. Answer – Option A

Explanation –

The pattern of the number series is:


5 + \({7}^{3}\) = 5 + 343 =348


348 + \({6}^{3}\) =348 + 216 =564


564 + \({5}^{3}\) = 564 + 125 = 689


689 + \({4}^{3}\) = 689 + 64 = 753, \(\neq\) [716]


753 + \({3}^{3}\) = 753 + 27 = 780

Direction: In the following number series, a wrong number is given. Find out that wrong number.


1. 6 91 5842935 1175635277 70558

    A. 6
    B. 70558
    C. 584
    D. 2935
    E. 35277


2. 8424 4212 2106 1051 526.5 263.25 131.625

    A. 526.5
    B. 1051
    C. 4212
    D. 8424
    E. 263.25


3. 850 600 550 500 475 462.5 456.25

    A. 600
    B. 550
    C. 500
    D. 462.5
    E. None of these


4. 9050 5675 3478 2147 14181077 950

    A. 950
    B. 1418
    C. 5675
    D. 2147
    E. 1077


5. 142 119 100 83 65 59 52

    A. 65
    B. 100
    C. 59
    D. 119
    E. None of these


Direction: In the following number series, a wrong number is given. Find out that wrong number.


6. 1 4 27 256 3125 46658

    A. 46658
    B. 4
    C. 27
    D. 3125
    E. None of these


7. ? 4.5 16 25 33 38.5 42 43.5

    A. 33
    B. 38.5
    C. 42
    D. 43.5
    E. 25


8. 1 2 12 63 316 1704 10446

    A. 63
    B. 1704
    C. 316
    D. 10446
    E. 2


9. 1 2 6 21 88 505 2676

    A. 505
    B. 88
    C. 2676
    D. 21
    E. 6


10. 1 2 12 63 316 1704 10446

    A. 63
    B. 1704
    C. 316
    D. 10446
    E. 2


Answers and Explanations


1. Answer – Option C

Explanation –

The pattern of the number series is:


6 × 7 + \({7}^{2}\) = 42 + 49 = 91


91 × 6 + \({6}^{2}\) = 546 + 36 = 582 \(\neq\)[584]


582 × 5 + \({5}^{2}\) = 2910 + 25 = 2935


2935 × 4 + \({4}^{2}\) = 11740 + 16 = 11756


11756 × 3 + \({3}^{2}\) = 35268 + 9 = 35277


2. Answer – Option B

Explanation –

The pattern of the number series is:


\(\frac{14824}{2}\) = 4212


\(\frac{4212}{2}\) = 2106


\(\frac{2106}{2}\) = 1053 \(\neq\)[1051]


\(\frac{1053}{2}\) = 526.5


\(\frac{526.5}{2}\) = 263.25


3. Answer – Option A

Explanation –

The pattern is:


850 – 200 = 650 \(\neq\) [600]


650 – 100 = 550


550 – 50 = 500


500 – 25 = 475


475 – 12.5 = 462.5


4. Answer – Option C

Explanation –

The pattern of the number series is:


9050 – \({15}^{3}\) = 9050 – 3375 = 5675


5675 – \({13}^{3}\) = 5675 – 2197 = 3478


3478 – \({11}^{3}\) = 3478 – 1331 = 2147


2147 – \({9}^{3}\) = 2147 – 729= 1418


1418 – \({7}^{3}\) = 1418 – 343 = 1075 \(\neq\) [1077]


5. Answer – Option A

Explanation –

The pattern is:


142 – 23 = 119


119 – 19 = 100


100 – 17 = 83


83 – 13 = 70 \(\neq\) [65]


70 – 11 = 59


59 – 7 = 52


6. Answer – Option A

Explanation –

The series is based on the following pattern:


\({1}^{1}\) = 1


\({2}^{2}\) = 4


\({3}^{3}\) = 27


\({4}^{4}\) = 256


\({5}^{5}\) = 3125


\({6}^{6}\) = [46656]


Hence, 46658 is the wrong number


7. Answer – Option E

Explanation –

The pattern of the number series is:


4.5 + 11.5 = 16


16 + 9.5 = 25.5 \(\neq\) [25]


25.5 + 7.5 = 33


33 + 5.5 = 38.5


8. Answer – Option

Explanation –

The pattern is:


1 × 1 + \({1}^{3}\) = 2


2 × 2 + \({2}^{3}\) = 12


12 × 3 + \({3}^{3}\) = 63


63 × 4 + \({4}^{3}\) = 316


316 × 5 + \({5}^{3}\) = 1705 \(\neq\) [1704]


9. Answer – Option A

Explanation –

The pattern is:


1 × 1 + 1 = 2


2 × 2 + 2 = 6


6 × 3 + 3 = 21


21 × 4 + 4 = 88


88 × 5 + 5 = 440 + 5 = 445


= 445 \(\neq\) [505]


445 × 6 + 6 = 2670 + 6 = 2676


10. Answer – Option B

Explanation –

The pattern is:


1 × 1 + \({1}^{3}\) = 2


2 × 2 + \({2}^{3}\) = 12


12 × 3 + \({3}^{3}\) = 63


63 × 4 + \({4}^{3}\) = 316


316 × 5 + \({5}^{3}\) = 1705 \(\neq\) [1704]

Direction: In the following number series, a wrong number is given. Find out that wrong number.


1. 1 3 6 11 20 39 70

    A. 3
    B. 39
    C. 11
    D. 20
    E. 6


2. 1 8 28 99 412 2075 12460

    A. 28
    B. 99
    C. 412
    D. 2075
    E. 12460


3. 10 8 13 35 135 671 4007

    A. 8
    B. 671
    C. 135
    D. 13
    E. 35


4. 11 14 22 37 68 96 144

    A. 37
    B. 68
    C. 96
    D. 22
    E. 144


5. 12 237 406 527 604 657

    A. 237
    B. 406
    C. 527
    D. 657
    E. None of these


Direction: In the following number series, a wrong number is given. Find out that wrong number.


6. 12000 2395 472 89.8 12.96 -2.408 -5.4816

    A. -5.4816
    B. 472
    C. 12.96
    D. – 2.408
    E. 2395


7. 125 75 45 25 16.2 9.72 5.832

    A. 25
    B. 45
    C. 9.72
    D. 16.2
    E. 75


8. 144 215 540 1890 8505 46777.5 304053.75

    A. 215
    B. 540
    C. 1890
    D. 8505
    E. 46777.5


9. 15 28 43 60 79 101 123

    A. 28
    B. 43
    C. 60
    D. 101`
    E. 123


10. 150 148 143 133 116 80 53

    A. 133
    B. 116
    C. 80
    D. 148
    E. 143


Answers and Explanations


1. Answer – Option D

Explanation –

The series is based on following pattern:


2 × 3 = 6


6 × 3 = 18


18 × 6 = 108 \(\div\)[109]


108 × 18 =1944


1944 × 108 = 209952


Hence, 109 is the wrong number and it should be replaced by 108.


2. Answer – Option

Explanation – E

The pattern of the given series is :


1 × 1 + 7 × 1 = 1 + 7


8 × 2 + 6 × 2 = 16 + 12 = 28


28 × 3 + 5 × 3 = 84 + 15 = 99


99 × 4 + 4 × 4 = 396 + 16 = 412


412 × 5 + 3 × 5 = 2060 + 15 = 2075


2075 × 6 + 2 × 6 = 12450 + 12


= 12462 \(\neq\)[12460]


3. Answer – Option C

Explanation –

The pattern is:


10 × 1 – 2 = 8


8 × 2 – 3 = 13


13 × 3 – 4 = 35


35 × 4 – 5 = 135


135 × 5 – 6 = 675 – 6


= 669 \(\neq\) [671]


669 × 6 – 7 = 4014 – 7 = 4007


4. Answer – Option B

Explanation –

The pattern is :


11 + 1 × 3 = 11 + 3 = 14


14 + 2 × 4 = 14 + 8 = 22


22 + 3 × 5 = 22 + 15 = 37


37 + 4 × 6 = 37 + 24 = 61 \(\neq\) [68]


61 + 5 × 7 = 61 + 35 = 96


96 + 6 × 8 = 96 + 48 = 144


5. Answer – Option E

Explanation –

The series is based on the following pattern:


12 + \({15}^{2}\) = 12 + 225 = 237


237 + \({13}^{2}\) = 237 + 169 = 406


406 + \({11}^{2}\) = 406 + 121 = 527


527 + \({9}^{2}\) = 527 + 81 = 608 \(\neq\) [604]


608 + \({7}^{2}\) = 608 + 49 = 657


Hence, 604 is the wrong number


6. Answer – Option B

Explanation –

The pattern of the given series is :


(\(\frac{12000}{5}\)) – 5 = 2400 – 5 = 2395


(\(\frac{2395}{5}\)) – 5 = 479 – 5 = 474 \(\neq\) [472]


(\(\frac{4474}{5}\)) – 5 = 94.8 – 5 = 89.8


(\(\frac{89.8}{5}\)) – 5 = 17.96 – 5 = 12.96


7. Answer – Option A

Explanation –

The pattern is:


125 × (\(\frac{3}{5}\)) =75


75 × (\(\frac{3}{5}\)) = 45


45 × (\(\frac{3}{5}\)) = 27 \(\neq\)[25]


27 × (\(\frac{3}{5}\)) = 16.2


16.2 × (\(\frac{3}{5}\)) = 9.72


8. Answer – Option A

Explanation –

The pattern of the given series is :


144 × 1.5 = 216 \(\neq\) [215]


216 × 2.5 = 540


540 × 3.5 = 1890


1890 × 4.5 = 8505


8505 × 5.5 = 46777.5


9. Answer – Option D

Explanation –

The pattern is:


15 + 13 = 28


28 + 15 = 43


43 + 17 = 60


60 + 19 = 79


79 + 21 = 100 \(\neq\) [101]


10. Answer – Option C

Explanation –

The pattern is:


150 – 2 = 148


148 – 5 = ( 2 + 3) = 143


143 – 10 = (5 + 5) = 133


133 – 17 = (10 + 7) = 116


116 – 26 = (17 + 9) = 90 \(\neq\) [80]


= 90 – 37 = (26 + 11) = 53

Direction: In the following number series, a wrong number is given. Find out that wrong number.


1. 16 19 21 30 46 71 107

    A. 19
    B. 21
    C. 30
    D. 46
    E. 71


2. 16 4 2 1.5 1.75 1.875

    A. 1.875
    B. 1.75
    C. 1.5
    D. 2
    E. 4


3. 17 17.25 18.25 20.75 24.5 30.75

    A. 23.25
    B. 24.25
    C. 24.5
    D. 24.75
    E. None of these


4. 18 119 708 3534 14136 42405

    A. 708
    B. 3534
    C. 14136
    D. 42405
    E. None of these


5. 18 21 2535 52 78 115

    A. 35
    B. 52
    C. 78
    D. 21
    E. 115


Direction: In the following number series, a wrong number is given. Find out that wrong number.


6. 18000 3600 720 142.2 28.8 5.76

    A. 28.8
    B. 3600
    C. 5.76
    D. 42.2
    E. None of these


7. 2 54 300 1220 3674 7350

    A. 3674
    B. 1220
    C. 300
    D. 54
    E. None of these


8. 2 13 27 113 561 3369 23581

    A. 13
    B. 27
    C. 113
    D. 561
    E. 3369


9. 2 3 11 38 102 229 443

    A. 11
    B. 229
    C. 102
    D. 38
    E. 3


10. 2 3 6 18 109 1944 209952

    A. 3
    B. 6
    C. 18
    D. 109
    E. 1944


Answers and Explanations


1. Answer – Option A

Explanation –

The series is based on the following pattern:


107 – 71 = 36 = \({6}^{2}\)


71 – 46 = 25 = \({5}^{2}\)


46 – 30 = 16 = \({4}^{2}\)


30 – 21 = 9 = \(3{}^{2}\)


21 – 19 = 2 \(\neq\) \({2}^{2}\)


19 should be replaced by 17 for which 21 – 17 = \({2}^{2}\)


2. Answer – Option B


3. Answer – Option B

Explanation –

The original series is based on following pattern:


17 + 0.25 × \({1}^{2}\) = 17.25


17.25 + 0.25 × \({2}^{2}\) = 18.25


18.25 + 0.25 × \({3}^{2}\) = [20.50]


20.50 + 0.25 × \({4}^{2}\) = 24.50


24.50 + 0.25 × \({5}^{2}\) = 30.75


Therefore, the number 20.75 is wrong. Hence, the new series is as follows:


20.75 + 0.25 × \({1}^{2}\) = 21.00 —— \({2}^{nd}\). term


21.00 + 0.25 × \({2}^{2}\) = 22.00 ——\({3}^{rd}\).term


22.00 + 2.25 × \({3}^{2}\) = 24.25 ——\({4}^{th}\) term


Therefore, the fourth term of the new series is 24.25


4. Answer – Option B

Explanation –

The series is based on the following pattern:


18 × 7 – 7 = 126 – 7 = 119


119 × 6 – 6 = 714 -708


708 × 5 – 5 = 3540 – 5 = 3535 \(\neq\) [3534]


3535 × 4 – 4 = 14140 – 4 = 14136


Hence 3534 is the wrong number.


5. Answer – Option C

Explanation –


The pattern is:


7 + \({1}^{3}\) = 7 + 1 = 8


8 + \({3}^{3}\) = 8 + 27 = 35


35 + \({5}^{3}\) = 35 + 125 = 160


160 + \({7}^{3}\) = 160 + 343 = 503 \(\neq\) [505]


503 + \({9}^{3}\) = 503 + 729 = 1232


1232 + \({11}^{3}\) = 1232 + 1331 = 2563


6. Answer – Option D

Explanation –

The series is based on the following pattern:


\(\frac{1800}{5}\) = 3600


\(\frac{3600}{5}\) = 720


\(\frac{720}{5}\) = 144 \(\neq\) [142.5]


\(\frac{144}{5}\) = 28.3


\(\frac{28.8}{5}\) = 5.76


Hence 142.5 is the wrong number.


7. Answer – Option A

Explanation –

2 × 6 + 7 × 6 = 12 + 42 = 54


54 × 5 + 6 × 5 = 270 + 30 = 300


300 × 4 + 5 × 4 = 1200 + 20 = 1220


1220 × 3 + 4 × 3 = 3660 + 12 = 3672 \(\neq\) [3674]


3672 × 2 + 3 × 2 = 7344 + 6 =7 350


8. Answer – Option A

Explanation –

The series is based on following pattern:


2 × 2 + 7 = 11 (not 13)


11 × 3 – 6 = 27


27 × 4 + 5 = 113


113 × 5 – 4 = 561


Obviously, the number 13 is wrong and it should be replaced with 11.


9. Answer – Option B

Explanation –

The sequence is based on following pattern:


3 – 2 = \({1}^{3}\)


11 – 3 = 8 = \({2}^{3}\)


38 – 11 = \({27}^{3}\)


102 – 38 = 64 = \({4}^{3}\)


But 229 – 102 = 127 \(\neq\) \({5}^{3}\)


227 – 102 = 125 = \({5}^{3}\)


443 – 227 = 125 = \({6}^{3}\)


Obviously 229 is the wrong number.


10. Answer – Option B

Direction: In the following number series, a wrong number is given. Find out that wrong number.


1. 2 4 5 8 13 21 34

    A. 4
    B. 5
    C. 8
    D. 13
    E. 21


2. 2 6 16 38 84 176 368

    A. 6
    B. 16
    C. 38
    D. 84
    E. 176


3. 2 6 24 96 285 568 567

    A. 6
    B. 96
    C. 24
    D. 568
    E. 567


4. 2 6 2496 285 568 567

    A. 6
    B. 96
    C. 24
    D. 568
    E. 567


5. 2 7 18 45 99 209 431

    A. 172
    B. 171
    C. 174
    D. 75
    E. None of these


Direction: In the following number series, a wrong number is given. Find out that wrong number.


6. 2222 1879 1663 1538 1474 1447 1440

    A. 1879
    B. 1538
    C. 1474
    D. 1447
    E. 1440


7. 3 10 33 111 349 1072 3252

    A. 33
    B. 111
    C. 349
    D. 1072
    E. 10


8. 3 10 33 111 349 1072 3252

    A. 33
    B. 111
    C. 349
    D. 1072
    E. 10


9. 3 35 226 1160 4660 13998

    A. 13998
    B. 4660
    C. 226
    D. 1160
    E.


10. 3 4 13 38 87 166 289

    A. 38
    B. 13
    C. 87
    D. 166
    E. 4


Answers and Explanations


1. Answer – Option A

Explanation –

The series is based on following pattern:


2 + 3 = 5


5 + 3 = 8


8 + 5 = 13


13 + 8 = 21


21 + 13 = 34


Obviously, the number 4 is wrong and it should be replaced with 3.


2. Answer – Option E


3. Answer – Option C

Explanation –

The pattern is:


2 × 6 – 6 = 6


6 × 5 – 5 = 25 \(\neq\) [24]


24 × 4 – 4 = 96


96 × 3 – 3 = 285


4. Answer – Option B

Explanation –

The pattern is:


2 × 6 – 6 = 6


6 × 5 – 5 = 25 \(\neq\) [24]


25 × 4 – 4 = 96


96 × 3 – 3 = 285


5. Answer – Option A

Explanation –

The original series is based on following pattern:


2 × 2 +3 = 7


7 × 2 + 5 = [19]


19 × 2 + 7 = 45


45 × 2 + 9 = 99


99 × 2 + 11 = 209


209 × 2 +13 = 431


Therefore, the number 18 is wrong. Hence, the new series is as follows:


18 × 2 + 3 = 39 ———\({2}^{nd}\). term


39 × 2 + 5 = 83 ——–\({3}^{rd}\) term


83 × 2 + 7 = [173 ——\({4}^{th}\) term]


173 × 2 + 9 = 355


Therefore, the fourth term of the new series is 173.


6. Answer – Option E

Explanation –

The pattern of the given series is :


2222 – \({7}^{3}\) = 2222 – 343 = 1879


1879 – 63 = 1879 – 216 = 1663


1663 – \({5}^{3}\) = 1663 – 125 = 1538


1538 – \({4}^{3}\) = 1538 – 64 = 1474


1474 – \({3}^{3}\) = 1474 – 27 = 1447


1447 – \({2}^{3}\) = 1447 – 8 = 1439 \(\neq\) [1440]


7. Answer – Option A

Explanation –

The pattern is:


3 × 3 + \({1}^{2}\) = 9 + 1 = 10


10 × 3 + \({2}^{2}\) = 30 + 4 = 34 \(\neq\) [33]


34 × 3 + \({3}^{2}\) = 102 + 9 = 111


111 × 3 + \({4}^{2}\) = 333 + 16 = 349


349 × 3 + \({5}^{2}\) = 1047 + 25 = 1072


8. Answer – Option A

Explanation –

The pattern is:


3 × 3 + \({1}^{2}\) = 9 + 1 = 10


10 × 3 + \({2}^{2}\) = 30 + 4 = 34 \(\neq\) [34]


34 × 3 + \({3}^{2}\) = 102 + 9 = 111


111 × 3 + \({4}^{2}\) = 333 + 16 = 349


349 × 3 + \({5}^{2}\) = 1047 + 25 = 1072


9. Answer – Option C

Explanation –

The series is based on the following pattern:


3 × 7 + 2 × 7 = 21 + 14 = 35


35 × 6 + 3 × 6= 210 + 18 = 228 \(\neq\) [226]


228 × 5 + 4 × 5 = 1140 + 20 = 1160


1160 × 4 + 5 × 4 = 4640 + 20 = 4660


4660 × 3 + 6 × 3 = 13980 + 18 = 13998


Hence, 226 is the wrong number.


10. Answer – Option D

Explanation –

The series is based on following pattern:


4 – 3 = \({2}^{2}\)


13 – 4 = 9 = \({3}^{2}\)


38 – 13 = 25 = \({5}^{2}\)


87 – 38 = 49 = \({7}^{2}\)


168 – 87 = 81 = \({9}^{2}\)


289 – 168 = 121 = \({11}^{2}\)


Obviously, 166 is wrong number.

Direction: In the following number series, a wrong number is given. Find out that wrong number.


1. 3 9 23 99 479 2881 20159

    A. 2881
    B. 9
    C. 23
    D. 99
    E. 479


2. 32 34 37 46 62 87 123

    A. 34
    B. 37
    C. 62
    D. 87
    E. 46


3. 33 321 465 537 573 590 600

    A. 321
    B. 465
    C. 573
    D. 537
    E. 590


4. 37 47 52 67 87 112 142

    A. 47
    B. 52
    C. 67
    D. 87
    E. 112


5. 4 2 3.5 7.5 26.25 118.125

    A. 118.125
    B. 26.25
    C. 3.5
    D. 2
    E. 7.5


Direction: In the following number series, a wrong number is given. Find out that wrong number.


6. 4 5 9 29 111 556 3325

    A. 5
    B. 9
    C. 29
    D. 111
    E. 556


7. 4 24 161 965 4795 19176 57525

    A. 161
    B. 965
    C. 57525
    D. 19176
    E. None of these


8. 4 3 4.5 8.5 20 53 162.5

    A. 3
    B. 4.5
    C. 8.5
    D. 20
    E. 53


9. 4 6 12 30 75 315 1260

    A. 315
    B. 75
    C. 12
    D. 6
    E. 30


10. 4444 2224 1114 556 281,5 142.75 73.375

    A. 2224
    B. 281.5
    C. 1114
    D. 556
    E. 142.75


Answers and Explanations


1. Answer – Option D

Explanation –

The series is based on following pattern:


3 × 2 + 3 = 9


9 × 3 – 4 = 23


23 × 4 + 5 = 97 (not 99)


97 × 5 – 6 = 479


Obviously, the number 99 is wrong and it should be replaced with 97.


2. Answer – Option A

Explanation –

The pattern of the number series is:


32 + \({1}^{2}\) = 32 + 1 = 33 \(\neq\) [34]


33 + \({2}^{2}\) = 33 + 4 = 37


37 + \({3}^{2}\) = 37 + 9 = 46


46 + \({4}^{2}\) = 46 + 16 = 62


62 + \({5}^{2}\) = 62 + 25 = 87


3. Answer – Option E

Explanation –

The pattern of the number series is:


33 + 288 = 321


321 + 144 = 465


465 + 72 = 537


537 + 36 = 573


573 + 18 = 591 \(\neq\) [590]


591 + 9 = 600


4. Answer – Option A

Explanation –

The pattern of the number series is:


37 + 1 × 5 = 42 \(\neq\) [47]


42 + 2 × 5 = 52


52 + 3 × 5 = 67


67 + 4 × 5 = 87


87 + 5 × 5 = 112


112 + 6 × 5 = 142


5. Answer – Option C


6. Answer – Option C


7. Answer – Option B

Explanation –


The pattern of the given series is :


The pattern is :


4 × 8 – 8 = 32 – 8 = 24


24 × 7 – 7 = 168 – 7 = 161


161 × 6 – 6 = 966 – 6 = 960 \(\neq\) [965]


960 × 5 – 5 = 4800 – 5 = 4795


8. Answer – Option

Explanation –

The pattern of the given series is :


4 × 0.5 + 1 = 2 + 1 = 3


3 × 1 + 1.5 = 3 + 1.5 = 4.5


4.5 × 1 + 2 = 6.75 + 2


= 8.75 \(\neq\) [8.5]


8.75 × 2 + 2.5 = 17.5 + 2.5 = 20


20 × 2.5 + 3 = 50 + 3 = 53


9. Answer – Option B


10. Answer – Option D

Explanation –

The pattern of the number series is:


(\(\frac{4444}{2}\)) + 2 = 2224


(\(\frac{2224}{2}\)) + 2 =1114


(\(\frac{1114}{2}\)) + 2 = 559 \(\neq\) [556]


(\(\frac{559}{2}\)) + 2 = 2815

Direction: In the following number series, a wrong number is given. Find out that wrong number.


1. 5 4 6 15 56 285 1644

    A. 56
    B. 285
    C. 6
    D. 15
    E. 4


2.50 51 47 56 42 65 29

    A. 51
    B. 47
    C. 56
    D. 42
    E. 65


3. 6 4 58.5 18 48 139

    A. 8.5
    B. 48
    C. 139
    D. 8.5
    E. 5


4. 6 49 305 1545 6196 18603 37218

    A. 6169
    B. 49
    C. 305
    D. 1547
    E. 18603


5. 6 7 9 13 26 37 69

    A. 7
    B. 26
    C. 69
    D. 37
    E. 9


Direction: In the following number series, a wrong number is given. Find out that wrong number.


6. 68 10 42 146 770 4578

    A. 868
    B. 8872
    C. 858
    D. 8872
    E. None of these


7. 7 8 35 160 505 1232 2563

    A. 335
    B. 160
    C. 505
    D. 1232
    E. 2563


8. 7 9 16 25 41 68 107 173

    A. 107
    B. 16
    C. 41
    D. 68
    E. 254


9. 7 18 40 106 183 282 403

    A. 18
    B. 282
    C. 40
    D. 106
    E. 183


10. 7 4 6 9 20 52.5 160.5

    A. 6
    B. 4
    C. 20
    D. 9
    E. 52.5


Answers and Explanations


1. Answer – Option B

Explanation –

The pattern is:


5 × 1 – 1 = 5 – 1 = 4


4 × 2 – 2 = 8 – 2 = 6


6 × 3 – 3 = 18 – 3 = 15


15 × 4 – 4 = 60 – 4 = 56


56 × 5 – 5 = 280 – 5 = 275 \(\neq\)[285]


275 × 6 – 6 = 1650 – 6 = 1644


2. Answer – Option D

Explanation –

The series is based on following pattern:


50 + \({1}^{2}\) = 51


51 – \({2}^{2}\) = 47


47 + \({3}^{2}\) = 56


56 – \({4}^{2}\) = 40 (not 42)


42 + \({5}^{2}\) = 65

Obviously, the number 42 wrong and it should be replace with 40.


3. Answer – Option B

Explanation –

The pattern is:


6 × 0.5 + 1 = 3 + 1 = 4


4 × 1 + 1= 4 + 1 = 5


5 × 1.5 + 1 = 7.5 + 1 = 8.5


8.5 × 2 + 1 = 17 + 1 = 18


18 × 2.5 + 1 = 45 + 1 = 46 \(\neq\) [48]


46 × 3 + 1 = 138 + 1 = 139


4. Answer – Option C

Explanation –

The pattern of the number series is:


6 × 7 + 1 × 7 = 49


49 × 6 + 2 × 6 = 306 \(\neq\) [305]


306 × 5 + 3 × 5= 1545


1545 × 4 + 4 × 4 = 6196


6196 × 3 + 5 × 3 = 18603


5. Answer – Option B

Explanation –

The pattern is :


6 + 1 = 7


7 + 1 × 2 = 9


9 + 2 × 2 = 13


13 + 8 = 21 \(\neq\) [26]


21 + 16 = 37


37 + 32 = 69


6. Answer – Option

Explanation –

The original series is based on following pattern:


6 × 1 + 1 × 2 = 8


8 × 2 + 2 × 3 = 10


10 × 3 + 3 × 4 = 42


42 × 4 – 4 × 5 = 148


148 × 5 + 5 × 6 = 770


770 × 6 – 6 × 7 = 4578


Therefore, the number 146 is wrong. Hence, the new series is as follows:


146 × 1 + 1 × 2 = 148 —- \({2}^{nd}\) term


148 × 2 – 2 × 3 = 290 —–\({3}^{rd}\). term


290 × 3 + 3 × 4 = [882 ——\({4}^{th}\). term]


7. Answer – Option D

Explanation –

The pattern is:


18 + 2 = 20 \(\neq\)[21]


20 + 5 = (2 + 3) = 25


25 + 10 = (5 + 5) = 35


35 + 17 = (10 + 7) = 52


52 + 26 = (17 + 9) = 78


78 + 37 = (26 + 1) = 115


8. Answer – Option A

Explanation –

The series is based on the following pattern:


16 + 9 = 7


25 = 16 + 9


41= 16 = 25


i.e, 68 \(\neq\) 25 + 41


9. Answer – Option C

Explanation –

The pattern of the number series is:


7 + 1 × 11 = 7 + 11 = 18


18 + 3 × 11 = 18 + 33 = 51 \(\neq\) [40]


51 + 5 × 11 = 51 + 55 = 106


106 + 7 × 11 = 106 + 77 = 183


183 + 9 × 11 = 183 + 99 = 282


10. Answer – Option A

Direction: In the following number series, a wrong number is given. Find out that wrong number.


1. 8 4 4 6 12 28 90

    A. 18
    B. 42
    C. 21
    D. 24
    E. None of these


2. 8 21 47 86 140 203 281

    A. 47
    B. 86
    C. 140
    D. 203
    E. None of these


3. 8 5 6.5 11 26 68 207.5

    A. 68
    B. 6.5
    C. 11
    D. 26
    E. 207.5


4. 9 10 18 45 109 235 450

    A. 10
    B. 9
    C. 18
    D. 109
    E. 235


5. 9 10 18 45 109 235 450

    A. 18
    B. 109
    C. 269
    D. 661
    E. 146


6. 950 661 436 269 146 65 16

    A. 436
    B. 65
    C. 269
    D. 661
    E. 146


Answers and Explanations


1. Answer – Option C

Explanation –

The original series is based on following pattern:


8 × (\(\frac{1}{2}\)) = 4


4 × 1 = 4


4 × 1.5 = 6


6 × 2 = 12


12 × 2.5 = [30]


30 × 3 = 90


Therefore, the number 28 is wrong. Hence, the new


series is as follows:


28 × (\(\frac{1}{2}\)) = 14 ……\({2}^{nd}\) term


14 × 1 = 14 ——–\({3}^{rd}\). term


14 × 1.5 = 21 – \({4}^{th}\) term.


21 × 2 = 42


Therefore, the fourth term of new series is 21.


2. Answer – Option c

Explanation –

The pattern is :

8 + 1 × 13 = 21


21 + 2 × 13 = 21 + 26 = 47


47 + 3 × 13 = 47 + 39 = 86


86 + 4 × 13 = 86 + 52 = 138 [140]


138 + 5 × 13 = 138 + 65 = 203


203 + 6 × 13 = 203 + 78 = 281


3. Answer – Option C

Explanation –

The pattern of the number series is:


8 × 0.5 + 1 = 5


5 × 1 + 1.5 = 6.5


6.5 × 1.5 + 2 = 9.75 + 2 = 11.75 \(\neq\) [11]


11.75 × 2 + 2.5 = 23.5 + 2.5 = 26


26 × 2.5 + 3 = 68


4. Answer – Option E

Explanation –

(e) The pattern is:


9 + \({1}^{3}\) = 10


10 + \({2}^{3}\) = 10 + 8 = 18


18 + \({3}^{3}\) = 18 + 27 = 45


45 + \({4}^{3}\) = 45 + 64 = 109


109 + \({5}^{3}\) = 109 + 125 = 234 \(\neq\) [235]


234 + \({6}^{3}\) = 234 + 216 = 450


5. Answer – Option E

Explanation –

The pattern is:


9 + \({1}^{3}\) = 10


10 + \({2}^{3}\) = 10 + 8 = 18


18 + \({3}^{3}\) = 18 + 27 = 45


45 + \({4}^{3}\) = 45 + 64 = 109


109 + \({5}^{3}\) = 109 + 125 = 234 \(\neq\) [235]


234 + \({6}^{3}\) = 234 + 216 = 450


6. Answer – Option E

Explanation –

The pattern is :


950 – 661 = 289 = \({17}^{2}\)


661 – 436 = 225 = \({15}^{2}\)


436 – [269] =167 \({13}^{2}\)


i.e, 436 – 267 = 167 = \(\neq\) \({13}^{2}\)


267 – 146 = 121 = \({11}^{2}\)


146 – 65 = 81 = \({9}^{2}\)