Understanding the Code Language Problem

This question asks us to decipher a specific code language where words are represented by numbers. We are given two examples: 'EACH' is coded as '97', and 'EASY' is coded as '64'. Our task is to find the code for 'ECHO' using the same pattern.

To solve this type of problem, we need to look for a relationship between the letters in the words and the given numerical codes. Common patterns involve the alphabetical positions of the letters.

Analysing the Coding Pattern for 'EACH'

Let's first consider the alphabetical positions of the letters in 'EACH':

• E is the 5th letter
• A is the 1st letter
• C is the 3rd letter
• H is the 8th letter

The sum of these positions is \(5 + 1 + 3 + 8 = 17\). This does not match the code '97'.

Another common pattern involves the reverse alphabetical positions. The reverse position of a letter is its position counted from Z (Z=1, Y=2, ..., A=26). Alternatively, the reverse position can be calculated as \(26 - \text{alphabetical position} + 1\).

Let's find the reverse alphabetical positions for 'EACH':

• E: \(26 - 5 + 1 = 22\)
• A: \(26 - 1 + 1 = 26\)
• C: \(26 - 3 + 1 = 24\)
• H: \(26 - 8 + 1 = 19\)

Now, let's sum these reverse positions:

\(22 + 26 + 24 + 19 = 91\)

The sum is 91, and the code is 97. The difference is \(97 - 91 = 6\). It seems a constant value might be added to the sum of reverse positions.

Verifying the Pattern with 'EASY'

Let's test this potential pattern with the second example, 'EASY', which is coded as '64'.

First, find the alphabetical positions:

• E = 5
• A = 1
• S = 19
• Y = 25

Sum of alphabetical positions: \(5 + 1 + 19 + 25 = 50\). This doesn't match 64.

Now, let's find the reverse alphabetical positions for 'EASY':

• E: \(26 - 5 + 1 = 22\)
• A: \(26 - 1 + 1 = 26\)
• S: \(26 - 19 + 1 = 8\)
• Y: \(26 - 25 + 1 = 2\)

Sum of reverse positions:

\(22 + 26 + 8 + 2 = 58\)

The sum is 58, and the code is 64. The difference is \(64 - 58 = 6\). This matches the difference found for 'EACH'.

So, the pattern is confirmed: The code is the sum of the reverse alphabetical positions of the letters plus 6.

Applying the Code Pattern to 'ECHO'

Now we can apply the established pattern to find the code for 'ECHO'.

First, find the alphabetical positions of the letters in 'ECHO':

• E = 5
• C = 3
• H = 8
• O = 15

Next, find the reverse alphabetical positions:

• E: \(26 - 5 + 1 = 22\)
• C: \(26 - 3 + 1 = 24\)
• H: \(26 - 8 + 1 = 19\)
• O: \(26 - 15 + 1 = 12\)

Now, sum these reverse positions:

\(22 + 24 + 19 + 12 = 77\)

Finally, apply the last step of the pattern: add 6 to the sum.

\(77 + 6 = 83\)

Therefore, the code for 'ECHO' is 83.

Comparing Calculated Code with Options

Let's compare our calculated code (83) with the given options:

• Option 1: 85
• Option 2: 82
• Option 3: 83
• Option 4: 86

Our calculated code, 83, matches Option 3.

Revision Table: Code Language Concepts

Additional Information on Coding-Decoding

Coding-decoding questions are common in logical reasoning sections of exams. They test your ability to identify patterns in how words, letters, or numbers are transformed. Here are some other patterns you might encounter:

• Sum or Difference of Positions: Simple addition or subtraction of alphabetical positions.
• Letter Shifting: Each letter is shifted a fixed number of positions forward or backward in the alphabet (e.g., A becomes C, B becomes D, etc.).
• Opposite Letters: Replacing letters with their counterparts from the other end of the alphabet (A with Z, B with Y, etc.).
• Consonant/Vowel Coding: Different rules might apply to consonants and vowels.
• Position Reversal: The order of letters or their corresponding codes might be reversed.
• Mathematical Operations: Squaring, cubing, or other operations on the positions or sums.

Practicing various types of coding-decoding problems helps you quickly identify the pattern during an exam.