### Alphabet Reasoning

While solving the problems based on the alphabet, you must have in your mind the exact positions of every letter of the alphabet in forward order as well as in backward or reverse order.

Letters positions in forward alphabetical order | ||||||||

A | B | C | D | E | F | G | H | I |

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

J | K | L | M | N | O | P | Q | R |

10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |

S | T | U | V | W | X | Y | Z | |

19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 |

### Trick to remember alphabetical order

CFILORUX | |||||||

C | F | I | L | O | R | U | X |

3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 |

Letters’ positions in forward alphabetical order can be remembered using the word ‘Cfilorux’.

**Example 1.**What will be the seventh letter from your left in the English alphabet?

**Solution:** Using the word ‘Cfilorux’ we know that ‘F’ = 6. Thus the seventh letter will be the next letter of ‘F’ i.e. ‘G’.

∴ 7 (seventh letter) = F + 1 ⇒ G

#### Reverse alphabetical order

The opposite letter of each letter may also be required while solving the questions, so, you should also memorize the opposite letter of each letter.

Letters positions in backward or reverse alphabetical order | ||||||||

A | B | C | D | E | F | G | H | I |

26 | 25 | 24 | 23 | 22 | 21 | 20 | 19 | 18 |

J | K | L | M | N | O | P | Q | R |

17 | 16 | 15 | 14 | 13 | 12 | 11 | 10 | 9 |

S | T | U | V | W | X | Y | Z | |

8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |

### Trick to remember the opposite letter

The letter opposite to each letter of the English alphabet can be found by the Addition Method.

As we know that English alphabet has 26 characters. Hence any two letters of the English alphabet are opposite to each other if the sum of the alphabetical order of those letters is 27.

For example: B = 2, Y = 25

∴ B + Y ⇒ 27

Thus, ‘B’ and ‘Y’ are opposite to each other.

Similarly, D = 4, W = 23

∴ D + W ⇒ 27

Thus, ‘D’ and ‘W’ are opposite to each other.

**Example 2.**What is the opposite letter of the letter ‘P’ in the English alphabet?

**Sol: **The order of ‘P’ in the English Alphabet is 16.

Thus, the opposite of P will be (27 – 16 = 11), i.e. K

#### When letters are deleted

How to solve problems when letters are dropped or deleted at regular intervals?

**Example 3. **If every 3rd letter from left to right of the English alphabet is deleted, then what would be the 6th letter from the left in the new series obtained?

**Solution:** H

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

We find the new series as given below:

It is clear, that the 6th letter from the left in the new series is H.

## Types of Problems

### 1. General Series of Alphabet

**Example 4. **Which of the following options is seventh to the right of the 13th letter from the left in a forward Alphabet series?

- R
- T
- V
- W

**Solution (2):** T

1st of all we will write the forward alphabet series as given below:

From the above series, it is clear that M is the 13th letter from left, and seventh to the right of M is T.

This type of problem can be solved through a quicker method.

**Rules for Quicker Method**

- (a) If both the directions are the same then subtraction of numbers takes place.
- (b) If the directions are opposite then the addition of numbers takes place.

Now, for solving the above example we apply this rule.

As we want to find out the 7th letter to the **right** of the 13th letter from the **left**. Here, the directions are opposite, hence the addition of numbers will apply.

Hence we add 7 + 13 = 20

Therefore, the answer will be 20th from the left, i.e. T.

#### Reversed Alphabet Series

While solving problems based on general series of alphabets, we come across various cases. In some cases, we see that the whole alphabet series is reversed but in some other cases 1st half of the series is reversed, or the second half of the series is reversed or many segments of the alphabet series are reversed.

**Example 5.**If the 1st segment of 8 letters of the alphabet is written in reverse order, then the 2nd segment of the next 8 letters of the alphabet is written in reverse order, after that the segment of the remaining 10 letters is written in reverse order. Then find out the 4th letter from the left in the new obtained series.

- E
- D
- W
- M

**Solution (1): **E

Just see the presentation given below:

The required answer is ‘E’ because ‘E’ is at the 4th position from the left in the new obtained series.

#### Quicker approach

It is clear that 4th letter from the left in the new obtained series falls into the **first segment** which has 8 letters.

Hence 4th letter in the new obtained series = (8 + 1 – 4) = 5th letter from the left in the original series. Hence Required answer is E.

**Example 6.**If the 1st segment of 8 letters of the alphabet is written in reverse order, then the 2nd segment of the next 8 letters of the alphabet is written in reverse order, after that the segment of the remaining 10 letters is written in reverse order. Then find out the 18th letter from the left in the new obtained series.

- L
- W
- Y
- X

**Solution (3): **Y

It is clear that the 18th letter from the left in the new obtained series is the **2nd letter** of the **3rd segment** (10 letters), hence it will be not affected by 1st two segments having 8 letters each (16 letters).

Then that will be 16 + (10 + 1 – 2) = 25th letter from the left in the original alphabet series which is Y.

#### Positions of letters are interchanged

How to solve if positions of letters are interchanged?

There is no rule for such types of problems. Only hard practice can give you the skill to solve such questions in a quick time.

**Example 7.**If A and C interchange their places, B and D interchange their places, F and H interchange their places, and so on, then which letter will be 5th to the left of Q?

- P
- N
- M
- T

**Solution (1): P**

As per the question, the interchanges take place as follows:

Here we can see that Q interchanges with S. Then to the left of Q, the 5th letter would be P because P interchanges with N.

#### How to find the middle letter?

**Case I:** Remember that if *m*th and *n*th letter from the left in the English alphabet are given then the middle letter

= th letter from the left.

**Example 8.**Which letter will be midway between the 8th letter from the left and the 16th letter from the left in the English alphabet?

- N
- M
- K
- L

**Solution (4): L**

Here *m* = 8 and *n* = 16; then middle letter

=

= 12th letter from the left in the alphabet, i.e., L

**Case II:** Remember that if *m*th and *n*th letter from the right in the English alphabet are given then the middle letter

= letter from right

letter from the left in the English alphabet.

**Example 9.**Which letter will be midway between 8th letter from the right and 16th letter from the right in the English alphabet.

- K
- O
- Q
- R

**Solution (2): O**

Here *m* = 8 and *n* = 16; then middle letter

= (27 – 12) = 15th letter from left, i.e., O

th letter from the left in the alphabet.

or middle letter = (27 – 12) = 15th letter from left = O

**Note:** In case I and case II (*m* + *n*) must be divisible by 2.

**Case III:** Remember that if the *m*th letter from the left and the *n*th letter from the right are given then the middle letter

= th letter from the left in the alphabet.

**Example 10.**Which letter will be midway between the 8th letter from the left and the 15th letter from the right?

- J
- I
- K
- L

**Solution (1): J**

Here m = 8 and n = 15; then middle letter

= 10th letter from the left in the English alphabet, i.e., J.

**Note:** In case III (*m* – *n*) + 27 must be divisible by 2.

### 2. Words in alphabetical order

In such types of questions, words are given and you have to find out which word will appear in the dictionary 1st or 2nd or 3rd or 4th, etc.

**Example 11.**Which of the following words will come 2nd in the dictionary?

- Name
- Shame
- Fame
- Came

**Solution (3): Fame**

‘Came’ comes 1st in the dictionary. ‘Fame’ comes 2nd in the dictionary. ‘Name’ comes 3rd in the dictionary. ‘Shame’ comes 4th in the dictionary.

∴ (3) is the required answer.

### 3. Problems of word formation

In such problems, a word is given and you have to find out the number of words to be formed out of some letters drawn from that particular word.

**Example 12.**How many meaningful words can be formed from the 3rd, 4th, 6th and 8th letters of the word ‘CONTROVERSIAL’?

- One
- Two
- More than two
- None

**Solution (2): Two**

Now from letters N T O and E, the two words ‘NOTE’ and ‘TONE’ can be formed.

### 4. Problems of letter gap

**Example 13.**How many pairs of letters are there in the word ‘DREAMLAND’ which have as many letters between them as in the English alphabet?

- One
- Three
- Four
- More than three

**Solution (3): Four**

Here, we are asked to solve problem according to the English alphabet. In this case, we have to count both ways. It does mean that we have to count from left to right and from right to left. Let us see the following presentation:

The above presentation makes it clear that the required pairs of letters are 4. (Pairs: DA, EA, ML and LN)

**Example 14. How many pairs of letters are there in the word ‘DREAMLAND’ which have the same number of letters between them as in the English alphabet in the same sequence.**

- One
- Three
- Four
- More than three

**Solution (1): One**

Here we are asked to solve problems according to the alphabetical sequence. It does mean that we have to do counting only from left to right. Let us see the following presentation:

The above presentation makes it clear that the required pair of letters is only one (Pair: LN)

## Solved Examples

**Example 15.**If alphabet series is given in backward or reverse order, then find out the eighth letter to the right of O?

- H
- G
- U
- X

**Solution (2): G**

It’s clear (2) is the correct answer.

Here ‘O’ is the 15th letter from the **right** and we have to find the eighth letter to the **right** of O. As per rule

Required letter is 15 – 8 = 7, i.e., G

**Example 16.**If the 1st half of the alphabet is written in reverse order, then find out the letter that would be the 20th letter from the right.

- G
- F
- D
- H

**Solution (1): G**

As the 2nd half is not reversed, the 1st 13 letters would be the same when we do counting from the right. But not letters coming after the 13th will be actually from the left.

Hence 14th letter from the right would be A; 15th would be B; 16th would be C and we move further in the same manner. Hence from the left which is G.

∴ Option (1) is the correct answer.

**Example 17.**Find out the word coming last in the dictionary.

- Large
- Long
- Lust
- Love

**Solution (3): Lust**

The correct arrangement is (1) Large (2) Long (3) Love (4) Lust.