Understanding the Coding Pattern

This question asks us to figure out a specific coding pattern used for words and then apply it to a new word. We are given two examples:

• CAB is coded as 6.
• BED is coded as 40.

We need to find how HAD will be coded based on this same pattern.

Analyzing the Examples: CAB and BED

Let's first assign a numerical value to each letter based on its position in the English alphabet (A=1, B=2, C=3, and so on).

Now let's look at the values for the letters in CAB and BED:

• CAB: C=3, A=1, B=2
• BED: B=2, E=5, D=4

We need to find an operation (or a combination of operations) that transforms the values (3, 1, 2) into 6 and the values (2, 5, 4) into 40.

Let's try some common operations:

• Sum of values:
  • CAB: $3 + 1 + 2 = 6$. This matches the code for CAB.
  • BED: $2 + 5 + 4 = 11$. This does not match the code 40 for BED. So, simple addition is not the rule.
• Product (Multiplication) of values:
  • CAB: $3 \times 1 \times 2 = 6$. This also matches the code for CAB.
  • BED: $2 \times 5 \times 4 = 40$. This matches the code for BED.

Since the product of the alphabetical values works for both CAB and BED, it is likely the coding pattern used in this question.

Applying the Pattern to HAD

Now we will apply the identified pattern (multiplying the alphabetical values of the letters) to the word HAD.

• H = 8
• A = 1
• D = 4

Let's calculate the product of these values:

$8 \times 1 \times 4 = 32$

Therefore, HAD is coded as 32.

Verifying the Answer

The calculated code for HAD is 32. Let's check the given options:

• Option 1: 32
• Option 2: 16
• Option 3: 52
• Option 4: 46

Our calculated value, 32, matches Option 1.

Summary of the Coding Logic

The coding logic involves assigning numerical values to letters based on their position in the alphabet (A=1, B=2, C=3, ...) and then multiplying these values together to get the code for the word.

Additional Information on Coding-Decoding

Coding and decoding questions are common in reasoning and aptitude tests. They test your ability to identify patterns and rules in how information is transformed. Common types of letter coding patterns include:

• Shifting Letters: Each letter is shifted a fixed number of positions forward or backward in the alphabet (e.g., A becomes C, B becomes D - a shift of +2).
• Reverse Alphabetical Order: Assigning values in reverse (Z=1, Y=2, ... A=26).
• Sum or Product of Values: As seen in this problem, using the numerical values and performing mathematical operations.
• Position Swapping: Letters within a word are rearranged based on a specific rule.
• Using Consonants/Vowels: Patterns might apply differently to vowels and consonants.
• Combination of Rules: Sometimes, more than one rule is used in sequence.

Practicing different types helps you quickly identify the pattern during an exam.