# Number Series

The **Reasoning** section of every competitive exam includes questions from the topic **Number Series**. This topic is considered to be quiet important and every year a good number of questions are asked from this topic.

**Number Series** is a form of numbers in a certain sequence, where some numbers are Mistakenly put into the series of numbers and some number is missing in that series, we need to observe first and then find the accurate number to that series of numbers.

**LearnFrenzy** provides you lots of fully solved ** "Number Series" **Questions and Answers with explanation.

**How to solve questions on "Number Series"?**

1. Questions on number series give you a series of numbers which are all connected to each other. Once you have ** identified** this pattern, solving the question becomes very simple.

2. This** pattern** can be of various kinds. Check the section below for a list of common patterns which are frequently present in the competitive examination.

3. Once you have ** identified** the pattern, apply it to the number before/ after the missing number in the series to get the desired answer.

**Common Patterns in "Number Series" Questions**

**1. Prime Numbers: ** When numbers are a series of prime numbers (a natural number which is greater than 1 and has no positive divisors other than 1 and the number itself)

For example - 11, 13, 17, 19...

**2. Squares/ Cubes: **When numbers are a series of perfect square or cube roots.

For example - 81, 100, 121, 144, 169...

**3. Patterns in differences**: Calculate the differences between the numbers given in the series provided in the question. Then try to observe the pattern in the new set of numbers that you have obtained after taking out the difference.

For example - 2, 5, 8, 11, 14... (here the difference between the numbers is 3, hence the next number will be 17)

**4. Pattern in Alternate Numbers:** When there is a pattern between every alternate or third number in the series

For example - 2, 9, 5, 12, 8 , 15, 11....

**5. Geometric Series:** When each successive number in the series is obtained by multiplying or dividing the previous number by a fixed number.

For example - 5, 45, 405, 3645

**6. Odd One Out:** When all but one number is part of a series

For example - 5, 10, 12, 15, 20... (Here all numbers except, 12 are multiples of 5)

**7. Pattern in Adjacent Number:** When adjacent numbers in the series changes based on a logical pattern.

For example - 2, 4, 12, 48... (Here the first number is multiplied by 2, the second number by 3 and the third number by 4)

**8. Complex Series:** In some patterns the differences between numbers is dynamic rather than being fixed, but there still is a clear logical rule.

For example - 3, 4, 6, 9, 13, 18.. (Here you can add 1 to the difference between two adjacent items. After the first number add 1, after the second number add 2 and after the third number you can add 3)

**9. Using Two or More Basic Arithmetic Functions:** In some series more than one operation (+, -, ÷, x) is used.

For example - 5, 7, 14, 16, 32... (here you can add 2, multiply by 2, add 2, multiply by 2, and so on)

**10. Cube Roots/ Square Roots:** When the number are a series of cube roots and square roots

For example - 512, 729, 1000... (here the next number in the series will be 1331)

**11. Alternate Primes:** Here the series is framed by taking the alternative prime numbers.

For example - 2, 5, 11, 17, 23, _, 41

After 23, the prime numbers are 29 and 31. So the answer is 31.

**12. Every Third number can be the sum of the preceding two numbers:**

For example - 3, 5, 8, 13, 21

Here starting from third number 3 + 5 = 8, 5 + 8 = 13, 8 + 13 = 21,

So, the answer is 13 + 21 = 34

## TIPS on cracking Reasoning Questions on Number Series

Tip #1:Arithmetic Series, Geometric Series, Patterns in Differences

(1) __Arithmetic Series__: When the differences between the successive numbers given in the series is the same. For example: 2, 5, 8, 11, 14... (Here the difference between the numbers is 3, hence the next number will be 17)

(2) __Geometric Series__: When each successive number in the series is obtained by multiplying or dividing the previous one by a fixed number. For example: 2, 6, 18, 72,…

(3) __Patterns in differences__:** **Calculate the differences between the numbers given in the series provided in the question. Then try to observe the pattern in the new set of numbers that you have obtained after taking out the difference.

** Question: **Look at this series: V, VIII, XI, XIV, __, XX, ... What number should fill the blank?

*Solution: *

This is an arithmetic series in Roman numerals; each no. is 3 more than the previous one. Thus, the missing number will be the *Roman equivalent of 20 – 3 = 17, i.e., XVII.*

** Question: **Look at this series: 201, 202, 204, 207, ... What number should come next?

*Solution: *

The difference between the successive numbers is 1, 2, 3 respectively. Thus, the difference keeps on increasing by 1. Thus, the next number in the series will be *207 + 4 = 211.*

Tip #2:Pattern in Alternate/Adjacent numbers

(1) __Pattern in Alternate numbers:__ When there is a pattern between every alternate or third number in the series. For example: 2, 9, 5, 12, 8 , 15, 11....

(2) __Pattern in adjacent number:__ When adjacent numbers in the series changes based on a logical pattern. For example: 2, 4, 12, 48... Here the numbers are being multiplied by 2, then by 3, then by 4 etc.

** Question:** Look at this series: F2, __, D8, C16, B32, ... What number should fill the blank?

*Solution: *

This is a complex series in which the successive letters decrease by 1 and the successive numbers are multiplied by 2. Thus, the number in the blank will be *E4.*

** Question: **Look carefully at the following series and choose the pair that comes next.

42 40 38 35 33 31 28

A. 25, 22 B. 26, 23 C. 26, 24 D. 25, 23

*Solution: *

This is an alternating subtraction series in which 2 is subtracted twice, then 3 is subtracted once, then 2 is subtracted twice, and so on. So the next terms in the following series will be 26 and 24. Thus the correct answer is* C.*

Tip #3:Prime Numbers, Squares/Cubes, Alternate primes/exponents

(1) __Squares/Cubes__: When numbers are a series of perfect squares. For example: 81, 100, 121, 144, 169...

(2) __Cube/Square roots__: When the numbers are a series of perfect cubes. For example: 512, 729, 1000...

(3) __Alternate Primes:__ Here the series is framed by taking the alternative prime numbers. For example: 2, 5, 11, 17, 23, 31…

** Question: **Look at this series: 4, 7, 16, 13, __, 19, 64, 29, ... What number should fill the blank?

*Solution: *

There are two alternating series here. The first one is the square of the multiples of 2 {2^{2}, 4^{2}, 6^{2}, 8^{2} …} and the second one is a series of alternating prime numbers. The missing number is a part of the first series so the missing number is *6*^{2}* = 36.*

** Question:** Look carefully at the following series and choose the pair that comes next.

4 7 26 10 13 20 16

A. 14, 17 B.** **18, 14 C. 19, 13 D.** **19, 14

*Solution: *

Two patterns alternate here, with every third number following the alternate pattern. In the main series, beginning with 4, 3 is added to each number to arrive at the next. In the alternating series, beginning with 26, 6 is subtracted from each number to arrive at the next. So the next numbers will be 16 + 3 = 19, 20 – 6 = 14. Thus, the correct answer is *D.*