# Number Series Practice Sets

5 Steps - 3 Clicks

# Number Series Practice Sets

### 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.

### 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

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

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

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

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

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

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

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

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

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

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

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 = $${9}^{2}$$