NUMBER SERIES

 
                                         NUMBER SERIES
1. 32 31 32 29 32 27 32 ? ?
A. 25 ,32
B. 31, 32
C. 29, 32
D. 25 ,30
Answer & Explanation
Answer: Option A
Explanation: This is an alternating repetition series. The number 32 alternates with a series in which each number decreases by 2.
 
2. 10 34 12 31 14 28 16 ? ?
A. 25 , 18
B. 30, 13
C. 19 ,26
D. 18 ,20
Answer: Option A
Explanation:Two patterns alternate here. The first pattern begins with 10 and adds 2 to each number to arrive at the next; the alternating pattern begins with 34 and subtracts 3 each time.
 
3. 34 30 26 22 18 14 10 ? ?
A. 8, 6
B. 6, 4
C. 14, 18
D. 6, 2
Answer: Option D
Explanation: This is a simple subtraction series, in which 4 is subtracted from each number to arrive at the next.

4. 2  44  4  41  6  38  8 ? ?
A. 10, 12
B. 35, 32
C. 34, 9
D. 35 ,10
Answer: Option D
Explanation: Here, there are two alternating patterns, one addition and one subtraction. The first starts with 2 and increases by 2; the second starts with 44 and decreases by 3.
 
 
5. 17  16  14  12  11  8  8 ?
1. 4
2. 7
3. 3
4. 2
Answer: Option 1
Explanation: There are two series:
Ist : 17 14 11 8 and 2nd: 16 12 8 ?
In first series, -3 , -3 ,-3….. and in 2nd series , -4 , -4 ,-4….
Therefore, next term will be 8 – 4 = 4.
 
6. 9 16 23 30 37 44 51 ? ?
A. 59 ,66
B. 56, 62
C. 58 ,66
D. 58, 65
Answer: Option D
Explanation: Here is a simple addition series, which begins with 9 and adds 7.
 
 
7. 17, 19, 23, 29, 31, 37, __
A. 47
B. 43
C. 40
D. 41
Answer: Option D
Explanation: The given numbers are consecutive prime numbers in increasing order starting with 17. Hence, the next number in the series is 41.
 

8. 54, 66, 82, 102, 126, __
A. 146
B. 130
C. 154
D. 144
Answer: Option C

Explanation:  54+12, 66+16, 82+20, 102+24, 126, __. The difference is increasing by 4, starting with 12. So, the next difference is 24 + 4 = 28.   Hence, the next number is 126 + 28 = 154.

 

9.3 2 2 5 5 5 7 8 8 9 11 11 ?

1. 12

2. 11

3. 9

4. 14

Sol: Option 2

Explanation: There are three parallel series going on in this question. The 1st, 4th, 7th terms are using logic of -1, 2nd, 5th and 8th terms are using logic of +1 and 3rd, 6th and 9th terms are using logic of +1 again. Answer will be 11, which belongs to 1st, 4th and 7th term.

 
 

10. 1 3 2 6 3 11 4 18 5 ?

1. 27

2. 25

3. 23

4. 29

Answer: Option 1
Explanation: CASE 1: 1+1=2 +1=3 +1=4 +1 =5,  CASE 2: 3 +3=6 +5=11 +7= 18 +9=27



11. 13 17 23 29 31 37 ?

1. 22

2. 41

3. 19

4. 23

Sol: Option 2
Explanation: The given series is a prime number series. Hence the next prime number in this sequence would be 41.

 

 

12. 2 3 10 38 172 (Find the wrong no. in this series)

1. 192

2. 10

3. 38

4. 2

Answer: Option 3
Explanation: Logic is 2×1 + 1 = 3, 3 × 2 + 4 =10, 10 × 3 + 9 = 39, 39 × 4 + 16 = 172…. So in place of 38, it should be 39.

 

 

13. 8 19 52 151 447 (Find the wrong no. in this series)

1. 19

2. 8

3. 52

4. 447

Sol: Option 4
Explanation: The logic is 8 × 3 – 5 = 19, 19 × 3 – 5 = 52, 52 × 3 – 5 = 151. So in place of 447, it should be 448.

 

 

14. 4 2 3  7.5  26.75 (Find the wrong no. in this series)

1. 26.75

2. 7.5

3. 3

4. 2

Sol: Option 1
Explanation: Logic is 4 × .5 = 2, 2 × 1.5 = 3, 3 × 2.5 = 7.5, 7.5 × 3.5 = 26.25 In place of 26.75, it should be 26.25.

 

15. 2 3 10 40 172  885  5346  (Find the wrong no. in this series)

1. 3

2. 885

3. 40

4. 172

Sol: Option 3
Explanation: Logic is 2 × 1 + 1 = 3, 3 × 2 + 4 = 10, 10 × 3 + 9 = 39. Thus the wrong number is 40,it should be 39.

 

16. 15 18 20 29 45 70 106 (Find the wrong no. in this series)

1.18

2.20

3.29

4.45

Sol: Option 1
Explanation: Starting from the back
106– 70 = 36, 70- 45 = 25, 45 – 29 = 16, 29 – 20 = 9, 20 – 16 = 4, 16 – 15 = 1. Every difference is perfect square starting from 36 and decreasing. Thus the wrong number is 18, it should be 16.

 
 

17. 11 14 20 29 40 56 (Find the wrong no. in this series)

1. 40

2. 4

3. 10

4. 19

Sol: Option 1
Explanation: Logic is that first difference is 3, next difference is 6, 9, so next should be 12 & 15. So instead of 40 the term should be 41

 

18. 49 50 46 55 38 64 28 (Find the wrong no. in this series)

1. 49

2. 46

3. 55

4. 38

Sol: Option 4
Explanation: Logic is 49 + 1 = 50, 50 – 4 = 46, 46 + 9 = 55, 55 – 16 = 39, 39 + 25 = 64. Thus the wrong number is 38, it should be 39.

 

19. 6 15 41 179 839 (Find the wrong no. in this series)

1. 15

2. 6

3. 179

4. 41

Sol: Option 3
Explanation: Logic is 6 × 2 + 3 = 15, 15 × 3 – 4 = 41, 41 × 4 + 5 = 169, 169 × 5 – 6 = 839
Thus the wrong number is 179, it should be 169.

 

20. 4 6 12 30 90  312.50   1260  (Find the wrong no. in this series)

1. 6

2. 90

3. 30

4. 312.50

Sol: Option 4
Explanation: Logic is 4 × 1.5 = 6, 6 × 2 = 12, 12 × 2.5 = 30, 30 × 3 = 90, 90 × 3.5 = 315, 315 × 4 = 1260. Thus the wrong number is 312.50, it should be 315.

 
 
 

21. 35 19 11 7 5  4.5 3.5 (Find the wrong no. in this series)

1. 4

2. 5

3. 11

4. 19

Sol: Option 1
Explanation: 35-19 = 16, 19-11 = 8, 11-7 = 4, 7-5 = 2, 5-4 = 1, 4-3.5 = .5 The difference is halved every time. Thus the wrong number is 4.5, it should be 4.

 

22.  5, 16, 49, 104, ?

A. 171

B. 191

C. 181

D. 161

Answer: C

Explanation: 5+11 =16, 16+33 =49, 49+55 =104, 104+77 =181.

 

23. 7, 26, 63, 124, 215, 342, ?

A. 481

B. 511

C. 391

B. 421

Answer: B

Explanation: Numbers are (2^3 – 1), (3^3 – 1), (4^3 – 1), (5^3 – 1), (6^3 – 1), (7^3 – 1) etc.

So, the next number is (8^3 – 1) = (512 – 1) = 511.

 

 

24. 3, 12, 27, 48, 75, 108, ?

A. 147
B. 183
C. 162
D. 192

ans. A

Explanation: The numbers are 3 x 1^2, 3 X 2^2, 3 X 3^2, 3 X 4^2, 3 X 5^2, 3 X 6^2, Missing number= 3 X 7^2 = 147

 

25.  1, 6, 13, 22, 33, ?

A. 44
B. 45
C. 46
D. 47

ans. c

The pattern is + 5, + 7, + 9, + 11,...

.'. Missing number = 33 + 13 = 46.

 

 

26. 3, 6, 18, 72, ?

A. 144
B. 360
C. 288
D. 216

ans. B

Explanation:  pattern is * 2, * 3,*4, number is = 72 x 5 = 360.

 

27. 3, 7, 6, 5, 9, 3, 12, 1, 15, ?

A. 18
B. 13
C. -1
D. 3

ans. c

Explanation: There are two series, beginning respectively with 3 and 7. In one 3 is added and in another 2 is subtracted. The next number is 1 – 2 = -1.

 

28. 2, 4, 12, 48, 240,?

A. 960
B. 1440
C. 1080
D. 1920

ans. B

Explanation: Go on multiplying the given numbers by 2, 3, 4, 5, 6.
So, the correct next number is 1440.

 

29. 3, 5, 5, 19, 7, 41, 9, ?

A) 71

B) 61

C) 79

D) 69

Answer: A) 71

Explanation: First series : 3, 5, 7, 9.   Second series : 5, 19, 41, ?

 Difference of Second series are 14, 22, 30 etc. Next term is 41+30 i.e equal to 71.

 

30.   132       156       ?         210          240          272

A) 196

B) 182

C) 199

D) 204

Answer: B) 182

Explanation: The given series follows a logic that 11 x 12, 12 x 13, 13 x 14, 14 x 15, 15 x 16,…. So the missing number is 13 x 14 = 182.

 

 

31. 1, 2, 6, 15, 31, 56, 91

A) 31

B) 15

C) 56

D) 91

Answer: D) 91

Explanation: The difference of the two consecutive numbers are 1, 4, 9, 16, 25, 35.

This is clearly , +(12), +(22), +(32), +(42), +(52),+(62) . Here 35 is wrong, So our wrong number is 91

 

 

32. 1, 2, 3, 10, ?, 9802

A) 99

B) 199

C) 299

D) 999

Answer: Option A

Explanation: 2 = 1^2 + 1, 3 = 2^2 − 1, 10 = 3^2 + 1. Now 10^2 − 1 = 99, 9802 = 99^2 + 1.

 

 

33. Find out the wrong term in the series 2, 3, 4, 4, 6, 8, 9, 12, 16

A) 9

B) 12

C) 16

D) 8

 Answer: A) 9

Explanation: The given sequence is a combination of three series:

i)1st, 4th, 7th terms i.e, 2, 4, 9

ii)2nd, 5th, 8th terms i.e, 3, 6, 12

iii)3rd, 6th, 9th terms i.e, 4, 8, 16

In each one of i, ii, iii, each term is twice the preceding term.

So, 9 is wrong and must be replaced by (4*2) = 8

 

  


34. 8, 15, 28, 53, ?, 199

A) 101

B) 102

C) 103

D) 104

Answer: Option B

Explanation: Here the series of the form is x2 − 1, x2 − 2,  x2 − 3,...

 53 x 2 - 4 = 106 - 4 = 102

 

35. 0, 7,  26,  63,  124,  ?

A) 125

B) 215

C) 512

D) 251

 Answer: B

 

 

36. 7, 8, 18, 57, ?, 1165, 6996

A) 228

B) 542

C) 232

D) 415

 Answer: Option C

Explanation: Here 2nd number = (1st number x 1 )+1

3rd number = (2nd number x 2 )+2

4th number = (3rd number x 3 )+3 and so on..

Therefore, 5th number = (4th number x 4) +4 =57 x 4 + 4 =232.

 

 37. 8, 27, 125, 343, 1381  (Find the wrong number in the given series.)

A) 27

B) 8

C) 343

D) 1381

Answer: D) 1381

Explanation: Given series follows Cubes on Prime Numbers i.e 23, 33, 53,...but  93 is 1331. so, 1381 is wrong.

 

38. Find the wrong number in the given series.

8, 27, 125, 343, 1381

A) 27

B) 8

C) 343

D) 1381

Answer: D) 1381

Explanation: Given series follows Cubes on Prime Numbers i.e 23, 33, 53,...but  93 is 1331. so 1381 is wrong

 

 39. Find out the wrong term in the series 0, 2, 3, 5, 8, 10, 15, 18, 24, 26, 35

A) 18

B) 35

C) 24

D) 8

Answer: A) 18

Explanation: The given sequence is a combination of two series:

i)0, 3, 8, 15, 24, 35

ii)2, 5, 10, 18, 26

The pattern in both i, ii is +3, +5, +7, . . . .

So, in ii) 18 is wrong and must be replaced by (10 + 7) = 17

 

40. Choose the correct alternative that will continue the same pattern and replace 'x' in series 4,9,25,x,121,169,289,361

A) 81

B) 36

C) 64

D) 49

Answer: D) 49

Explanation:  The given series consists of squares of consecutive prime numbers

2*2, 3*3, 5*5,  . . . . , 11*11, 13*13, 17*17

 

41. Find the next number in the given sequence?

11, 17, 39, 85, ?

A) 133

B) 143

C) 153

D) 163

 Answer: D) 163

Explanation: Her the given number series is 11, 17, 39, 85, ?

1111 + (32 − 3) = 1717 + (52 − 3) = 3939 + (72 − 3) = 8585 + (92 − 3) = 163

Hence, the next number in the given sequence is 163.

 

42. Find out the wrong term in the series 3, 7, 15, 39, 63, 127, 255, 511

A) 39

B) 255

C) 127

D) 63

Answer: A) 39

Explanation: The correct pattern is *2+1

So, 39 is wrong and must be replaced by (15 * 2 + 1) = 31

 

Which Number would come in place of the underline mark in the series.

43.    3, 9, 21, ___ , 93

A) 39

B) 45

C) 48

D) 51

 Answer: B) 45

Explanation: First difference is 6 and second is 12. But if we take third as 18, then fourth difference will be 24. Then 93 can not be the last term. So we have to take the difference as 6, 12, 24 and 48.

So Answer is 21+24 = 45

 

44. 3,14,58,234,938,?

1 : 4152

2 : 4110

3 : 3754

4 : 4154

Answer- 3 (3754)

Explanation- x4+2

 

45. 3,25,255,2545,25455, ?

1 : 254550

2 : 254555

3 : 254545

4 : 254555

Answer-3 (254545)

Explanation- 25=(3×10)-5

255=(25×10)+5

2545=(255×10)-5

25455=(2545×10)+5

?=(2545×10)-5 = 254545

 

46. 4725,1050,300,120,80,?

1 : 40

2 : 160

3 : 120

4 : 110

Answer-2 (160)

Explanation- 4725 / 4.5=1050

1050/3.5=300

300/2.5=120

120/1.5=80

80/0.5=160

 

47. 76 , 43 , 13 ,………

1.3

2.4

3.11

4.6

Answer – 2 . 4

Explanation – (7×6)+1=43 ; (1×3)+1=4

 

48. 6, 7, 16, 51, …………..

1.258

2.254

3.208

4.234

Answer – 3. 208

Explanation –  (6×1)+1=7; (7×2)+2=16;  (16*3)+3=51;  (51×4)+4=208

 

49. 2 , 30 , 130 , 350 , ………….

1.738

2.783

3.638

4.530

Answer – 1. 738

Explanation –  ( 1^3)+1=2; (3^3)+3=30  (5^3)+5=130   (7^3)+7=350   (9^3)+9=738

 

50. 3 , 10 , 20 , 27 , 54 , 61,…….

1.68

2.122

3.105

4.72

Answer – 2. 122

Explanation –  3+7=10; 10+10=20 20+7=27  27+27=54 54+7=61; 61+61=122

 

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