Series
Number Series:
Identify the pattern and apply it to the number before / after the missing number in the series to get the right answer.
Number Series Patterns:
- Prime Numbers: Given below is a series of prime numbers.
Example: 11, 13, 17, 19… - Squares / Cubes of numbers: Given below are examples of perfect squares and cubes.
Example:
Square of number: 92 = 81, 102 = 100, 112 = 121, 122 = 144, 132 = 169…
Cube of number: 43 = 64, 53 = 125, 63 = 216, 73 = 343… - Patterns in differences: Calculate the difference between the given numbers in the series.
Example: 2, 5, 8, 11, 14… (The difference between the numbers here is 3, hence the next number will be 17.) - Geometric Series: It is a case where each successive number in the series is obtained by multiplying or dividing the previous number by a fixed number.
Example: 5, 45, 405, 3645 - Odd One Out: When one number is not a part of a series, for example: 5, 10, 12, 15, 20… (Here all numbers, except 12, are multiples of 5.)
- n2 − 1 Series: Example: 0, 3, 8, 15, 24, 35, 48, …
- n2 + 1 Series: Example: 2, 5, 10, 17, 26, 37, …, 65.
- The middle digit is the sum of the other two digits. Example: 165, 121, etc.
Letter Series
While solving the problems based on alphabets, please remember the exact position of every letter in forward as well as in backward or reverse orders, as given below:
Positions of letters in forward alphabetical order:
| A | B | C | D | E | F | G | H | I | J | K | L | M |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
| N | O | P | Q | R | S | T | U | V | W | X | Y | Z |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 |
Positions of letters in backward or reverse alphabetical order:
| Z | Y | X | W | V | U | T | S | R | Q | P | O | N |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
| M | L | K | J | I | H | G | F | E | D | C | B | A |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 |
Here, the mth element counted from left to right of a series of x characters is equal to the (x + 1 − m)th element counted from right to left of that series.
Example:
Counting from left to right, find the position of J in the above given series.
Position of J in the English alphabet from left to right is 10. Thus m = 10.
Position of J from right to left would be (26 + 1 − 10) = 17.
The first half of the alphabet series is from A to M, i.e., 1–13, and the second half is from N to Z, i.e., 14–26.
Tricks:
I. EJOTY: You can locate the position of the letters easily and quickly (from left to right), using the trick called EJOTY.
| E | J | O | T | Y |
|---|---|---|---|---|
| 5 | 10 | 15 | 20 | 25 |
