Solving Number Series Problems

A series is a logical arrangement of figures, numbers, words, or alphabets. A number series is a collection of numbers that follow a specific pattern. Some specific pre-determined rules are concealed in number series questions, and the candidate must identify them to arrive at the proper answer.                       

Consider the numbers 1, 4, 7, 10, 13,…. The difference between the two successive numbers is three in this case. It’s worth noting that in a number series, every number except the first is related to the previous number according to a set of rules.

Series of Perfect Squares

First, let’s define the perfect square. If we take the square of an integer number, we get a perfect square number. To put it another way, we can say that when we square an integer, the outcome is always a perfect square. All whole numbers and their negative numbers are referred to as integers.

Examples:

1) Check whether 441 is a perfect square.

Sol: We can check with the help of factorization method, 

441 = 3 x 3 x 7 x 7 

Both numbers exist two times, we can multiply both of them 

21 x 21 = (21)²

Hence, 441 is a perfect square. 

2)Which of the following sequences is neither a perfect square series nor a derivative of a perfect square series?

1) 1, 1, 1, 1

 2) 2, 2, 2, 2

 3) 3, 6, 30, 870

 4) 3, 3, 3, 3

Ans: 4) 3, 3, 3, 3

The Two-Stage Type Series:

The Two-Stage Type Series is a set of phrases in which the difference between them produces a new series. In such a series, we have a parent series whose terms alter on a regular basis. The difference between each successive term of the parent series creates its own arithmetic progression.

Odd man out and series:

This topic is dependent on all of the fundamental principles we’ve covered so far in this aptitude session. A.P./G.P., squares and cube roots, binomial theorem, and so on.

Being logical and boosting your intelligence will assist you in handling odd man out and series of problems. Your approach to solving these difficulties should be distinct. Because time is limited, different problems relating to alphabets, numbers, metals, and so on can be asked. As a result, different rules and differences must be figured out rapidly to answer.

Questions:

1)3, 6, 11, 18, 27, ?, 51 (based on addition series)

Sol:

3 + 3 Equals 6

6 + 5 = 11

11 + 7 = 18

18 + 9 = 27

27 +11 = 38

38 + 13 = 51

As a result, the right response is 38.

2)50, 45, 40, 35, 30, ? (based on a succession of subtraction)

Sol:

50 – 5 = 45

45 – 5 = 40

40 – 5 = 35

35 – 5 = 30

30 – 5 =25

As a result, the right response is 25.

3)5, 11, 24.2, 53.24, ?, 257.6816 (based on multiplication series)

Sol:

5 x 2.2 = 11

11 x 2.2 = 24.2

24.2 x 2.2 = 53.24

53.24 x 2.2 = 117.128

117.128 x 2.2 = 257.6816

As a result, 117.128 is the correct answer.

4)4096, 1024, 256, ?, 16, 4 (based on division series)

Sol:

4096 / 4 = 1024

1024 / 4 = 256

256 / 4 = 64

64 / 4 = 16

16 / 4 = 4

As a result, the proper response is 64.

5)9, 16, 25, 36, 125, 169, 196, 225

1. 36
2. 196
3. 169
4. 125

Correct Answer: (d)

Except for 125, all of the numbers are perfect squares.

53 = 125

As a result, 125 is the odd number.

6)121, 275, 396, 385, 891, 932

1. 275
2. 396
3. 891

1. 932

Correct Answer: (d)

The sum of the other two digits is the middle digit.

121, 275, 396, 385, 891 all these numbers have middle digit as the sum of other two digits.

As a result, the answer is 932.

7)3, 5, 7, 14, 17, 19

1. 3
2. 7
3. 14
4. 17

Correct Answer: (c)

Except for 14, all of the numbers are prime.

As a result, 14 is the odd number.

8) Which one of the following is odd one out

 6, 9, 11,18, 14, 15

1. 9
2. 11
3. 14
4. 25

Correct Answer: (b)

Except for 11, each number is composite.

As a result, the odd number is 11.

9)9, 12, 17, 20, 25, 28, 34, 36, 41

1. 25
2. 28
3. 34
4. 41

Correct Answer: c

The differences between two consecutive numbers starting at 3 are 3, 5, 3, 5…

The phrase 34 is incorrect since the next number should differ by 5, i.e. the number should be 33.

As a result, 34 is the odd number.

Conclusion:

Perfect squares are useful because they show how to calculate the square root of a completely accurate natural number. A natural number, that is, a non-decimal, non-fractional integer, must also be the square root of a perfect square.

In many aspects of people’s lives, sequences and series play a vital role. They help in decision making by assisting us in predicting, evaluating, and monitoring the outcome of a situation or event.