Number Series

Number Series is a sequence formed out of numbers. In the number series questions, we have to detect the rules that result in the formation of a number series.
Number series is very important for all compitative exams . A chunk of Questions is asked from number series in compitative exams like Bank Clerk, Bank PO, SSC, PCS,CSAT .

Type of questions asked from number series

1. Find missing Number in the given series.

2. Find wrong number in the given series which does not follow the pattern.

3.The questions based on the 2 or more series .
    a) The series-I satisfy a certain pattern,then find a missing number in series- II  by using  the same pattern in Series-I.
    b) The series-I satisfy a certain pattern,then find a missing number in series- II  by using  the same pattern in Series-I.

In this study notes we will discuss question based on two or more series:

Directions (1-5) : The questions below are based on the given Series-I. The series-I satisfy a certain pattern, follow the same pattern in Series-II and answer the questions given below.

Question 1:

I)            126         1457       728         1071       946         973
II)            23           *              *              *              *              ?

a) 961                                    b) 689                                    c) 790                                    d) 870                    e) 890

Solution:

Series I pattern:

126 + 11³ = 1457

1457 – 9³ = 728

728 + 7³ = 1071

1071 – 5³ = 946

946 + 3³ = 973

Series II pattern:

23 + 11³ = 1354

1354 – 9³ = 625

625 + 7³ = 968

968 – 5³ = 843

843 + 3³ = 870

The answer is, 870

Question 2:         
I)             12           25           127         887         7439      

II)            55              ?         471          2951        23951   

a) 121                                    b) 119                                    c) 113                                    d) 117                    e) 111

Solution:

Series I pattern:
12*2 + 1³ = 25
25*4 + 3³ = 127
127*6 + 5³ = 887
887*8 + 7³ = 7439

Series II pattern:
55*2 + 1³ = 111
111*4 + 3³ = 471
471*6 + 5³ = 2951
2951*8 + 7³ = 23951
The answer is, 111

Question 3:

I)             3402       1377       540         207         78           29

II)            ?              *              *              *              99           *

a) 4852                                  b) 5103                                  c) 5376                                  d) 4527                  e) 3964

Solution:

Series I pattern:
3402 ÷ 3 + 3⁵ = 1377
1377 ÷ 3 + 3⁴ = 540
540 ÷ 3 + 3³ = 207
207 ÷ 3 + 3² = 78
78 ÷ 3 + 3¹ = 29

Series II pattern:
5103 ÷ 3 + 3⁵ = 1944
1944 ÷ 3 + 3⁴ = 729
729 ÷ 3 + 3³ = 270
270 ÷ 3 + 3² = 99
99 ÷ 3 + 3¹ = 36
The answer is, 5103

Directions : The questions below are based on the given Series-I. The series-I satisfy a certain pattern, follow the same pattern in Series-II and find the wrong number in the series –II.

Question 4:         

I. 88, 44, 44, 66, 132, 330, 990

II. 96, 48, 48, 72, 144, 360, ?

a) 48                                       b) 72                                      c) 144                                    d) 360                                    e) 1008

Solution:

Series- I pattern:
88 * 0.5 = 44
44 * 1 = 44
44 * 1.5 = 66
66 * 2 = 132
132 * 2.5 = 330
330 * 3 = 990

Series –II pattern:
96 * 0.5 = 48
48 * 1 = 48
48 * 1.5 = 72
72 * 2 = 144
144 * 2.5 = 360
360 * 3 = 1080
The wrong number is, 1008

Directions (5-6): A number is bolded in the series I, II and III. Find the wrong series which does not satisfies the given number and choose the options accordingly.

Question 5:    

I. 79, 200, 369, 594, 883, 1244

II. 1365, 1509, 1313, 1569, 1244, 1645

III. 3171, 3046, 2830, 2487, 1975, 1244

a) Both I and II                     b) Only I                                c) Only III                             d) Both II and III e) None

Solution:

Series – I pattern:
79 + 121 (11²) = 200
200 + 169 (13²) = 369
369 + 225 (15²) = 594
594 + 289 (17²) = 883
883 + 361 (19²) = 1244
The bolded number is followed the given series.

Series – II pattern:
1365 + 144 (12²) = 1509
1509 – 196 (14²) = 1313
1313 + 256 (16²) = 1569
1569 – 324 (18²) = 1245
1245 + 400 (20²) = 1645
The bolded number is not followed the given series.

Series – III pattern:
3171 – 125 (5³) = 3046
3046 – 216 (6³) = 2830
2830 – 343 (7³) = 2487
2487 – 512 (8³) = 1975
1975 – 729 (9³) = 1246
The bolded number is not followed the given series.

Question 6: Find in the following series BOLDED number is following or not  ? 

I. 24, 25, 54, 159, 640, 3205

II. 12, 26, 54, 110, 222, 446

III. 12, 13, 28, 29, 54, 61, 124, 125

a) Only II                                               b) Only III                             c) Both I and III                    d) Only I                e) None

Series – I pattern:
24 * 1 + 1 = 25
25 * 2 + 2 = 52
52 * 3 + 3 = 159
159 * 4 + 4 = 640
640 * 5 + 5 = 3205
The bolded number is not followed the given series.

Series – II pattern:
12 * 2 + 2 = 26
26 *2 + 2 = 54
54 * 2 + 2 = 110
110 * 2 + 2 = 222
222 * 2 + 2 = 446
The bolded number is followed the given series.

Series – III pattern:
12 * 1 + 1 = 13
13 * 2 + 2 = 28
28 * 1 + 1 = 29
29 * 2 + 2 = 60
60 * 1 + 1 = 61
61 * 2 + 2 = 124
124 * 1 + 1 = 125
The bolded number is not followed the given series.